Stability and stabilization of nonlinear system-Chapter 8非线性系统稳定性和稳定化
The effects of Tween 20 and sucrose on the stability of anti-L-selectin during lyophilization
The Effects of Tween 20and Sucrose on the Stability of Anti-L-Selectin during Lyophilization and ReconstitutionLATOYA S.JONES,1THEODORE W.RANDOLPH,2ULRICH KOHNERT,3APOLLON PAPADIMITRIOU,3G.WINTER,3MARIE-LUISE HAGMANN,3MARK C.MANNING,1JOHN F.CARPENTER 11School of Pharmacy,University of Colorado Health Sciences Center,Denver,Colorado 802622Department of Chemical Engineering,University of Colorado at Boulder,Boulder,Colorado 803093Boehringer Mannheim,Penzberg,GermanyReceived 19December 2000;revised 24May 2001;accepted 25May 2001ABSTRACT:We have chosen an anti-L-selectin antibody as a model protein to investigate the effects of sucrose and/or Tween 20on protein stability during lyophilization and reconstitution.Native anti-L-selectin secondary structure is substantially retained during lyophilization in the presence of sucrose (1or 0.125%).However,aggregation of the protein during reconstitution of lyophilized protein powders prepared without sucrose is not reduced by the presence of sucrose in the reconstitution medium.Aggregate formation upon reconstitution is completely inhibited by freeze drying the protein with sucrose and reconstituting with a 0.1%Tween 20solution.Tween 20(0.1%)also partially inhibits loss of native anti-L-selectin secondary structure during lyophilization.However,upon reconstitution the formula-tions lyophilized with Tween 20contain the highest levels of aggregates.The presence of Tween in only the reconstitution solution appears to inhibit the transition from dimers to higher order oligomers.Potential mechanism(s)for the Tween 20effects were investigated.However,no evidence of thermodynamic stabilization of anti-L-selectin conformation (e.g.,by Tween 20binding)could be detected.ß2001Wiley-Liss,Inc.and theAmerican Pharmaceutical Association J Pharm Sci 90:1466±1477,2001Keywords:lyophilization;reconstitution;antibody formulation;infrared spectro-scopy;protein aggregationINTRODUCTIONTo optimize protein stability during storage and shipping,lyophilized formulations are often employed.However,a lyophilized product has itsdrawbacks:the possibility for protein denatura-tion exists during both the freeze drying 1±6and reconstitution 7,8processes.Excipients are often critical for maintaining native protein con-formation during freezing and drying,and mini-mizing levels of protein aggregation in the reconstituted product.2±5,9±14The purpose of the present study is to investigate the effects of Tween 20and sucrose on the stability of an anti-L-selectin antibody during lyophilization and reconstitution.Lyophilization involves both freezing and dehydration steps,each capable of promoting protein denaturation.Sucrose inhibits protein un-folding during freezing and drying.1,5,6,9,12,15±18However,studies of structural preservation of1466JOURNAL OF PHARMACEUTICAL SCIENCES,VOL.90,NO.10,OCTOBER 2001Ulrich Kohnert's present address is Scil Biomedicals GmbH,Fraunhofer Str.15,D-82152,Martinsried,Germany.Apollon Papadimitriou's present address is Roche Diagnos-tics GmbH,Pharma Research,Penzberg,Germany.G.Winter's present address is Lehrstuhl fu Èr Pharmazeu-tische Technologie und Biopharmazie,Ludwig MaximiliansUniversita Èt Mu Ènchen,Germany.Correspondence to :J.F.Carpenter (Telephone:303-315-6075;Fax:303-315-6281;E-mail:john.carpenter@)Journal of Pharmaceutical Sciences,Vol.90,1466±1477(2001)ß2001Wiley-Liss,Inc.and the American Pharmaceutical Associationantibodies during lyophilization are limited.19 During freezing,sucrose inhibits protein denaturation by increasing the free energy of protein unfolding.20±22During dehydration, sucrose stabilizes a protein by replacing the hydrogen bonds between the protein and water molecules that are lost during drying.1,23The current study employs infrared spectroscopy to characterize the secondary structure of anti-L-selectin in the initial aqueous and lyophilized states.The experiments test the hypothesis that sucrose inhibits lyophilization-induced unfolding. The stabilization of proteins by surfactants is often attributed to limiting the extent of protein adsorption at various potentially denaturing interfaces(e.g.,ice/liquid,air/liquid,vial/ liquid).14,24±27In addition,nonionic surfactants can stabilize some proteins,such as human growth hormone24,29,30and tissue factor,28by binding to solvent exposed hydrophobic regions of the native state protein.Surfactants have been shown to inhibit protein denaturation during freeze thawing.3,15,18,26However,unlike excipi-ents such as sucrose,surfactants have a limited capacity to inhibit lyophilization-induced unfold-ing via the water replacement mechanism. Accordingly,Kreilgaard et al.found that Tween 20(0.002%)did not inhibit lyophilization-induced unfolding of Factor XIII.5In contrast,Chang et al. found that Tween80(0.1%)partially inhibited lyophilization-induced unfolding/aggregation of interleukin-1receptor antagonist,but this study was conducted under grossly destabilizing condi-tions that led to50%aggregation after reconstitu-tion.3There appears to be no published study that directly determines the effect of nonionic surfac-tants on the lyophilization-induced unfolding of antibodies.Thus,a second goal of the current study is to test the hypothesis that Tween20 should not inhibit the lyophilization-induced unfolding of anti-L-selectin.Lyophilized drugs must be reconstituted prior to administration.Aggregates have been pro-posed to form during reconstitution from a fraction of nonnative protein molecules that are present in the dried solid.17Minimizing protein unfolding during lyophilization by inclusion of excipients such as sucrose can reduce the level of aggregates present after reconstitution.16,31,32 Inclusion of surfactants(e.g.,Tween20)in the reconstitution solution might alter kinetics to favor refolding over aggregation.Typically,water alone is used to reconstitute the lyophilized product.Prestrelski et al.found that someexcipients(e.g.,0.1and0.5%Tween20,0.05% EDTA)in the reconstitution solutions reduced aggregation of keratinocyte growth factor and interleukin-2,whereas others(e.g.,N-octylgluco-side,Pluronic)had no signi®cant effect on keratinocyte growth factor but promoted aggrega-tion of interleukin-2.7,8They also found that additives in the reconstitution medium decreased the amount of soluble ribonuclease A aggregates.8 These studies focused only on proteins that had been stored at458C for2or more weeks, prior to reconstitution.7,8There are two published reports on the effects of surfactant solution on reconstitution of proteins immediately after lyo-philization.Chang et al.report that the presence of0.1%Tween80in the reconstitution medium decreased aggregation of interleukin1-receptor antagonist.3A reconstitution solution of0.02% Tween80was equally as effective at inhibiting aggregation of bovine IgG as the inclusion of either0.02or0.1%Tween80in the initial lyophilized formulation.14However,separate effects of the surfactant on inhibiting lyophiliza-tion-induced unfolding and fostering refolding during reconstitution were not tested.We hypothesize that,although Tween20might not completely inhibit structural perturbations of the protein during lyophilization,it will foster reduced levels of aggregation during reconstitu-tion.Furthermore,the effects of low concentra-tions of sucrose in the reconstitution solution will be evaluated.EXPERIMENTAL SECTIONMaterialsPuri®ed anti-L-selectin antibody was produced by Boehringer Mannheim(Mannheim,Germany) and was stored atÀ808C until needed.The protein is a humanized murine IgG4antibody.Upon thawing and dialysis,our SE-HPLC analy-sis(see below)revealed approximately98% monomer and2%dimer.Potassium phosphate monobasic,potassium phosphate dibasic,guani-dine hydrochloride(GdnHCl),infrared grade potassium bromide(KBr),and Tween20(Sigma Ultra)were purchased from Sigma Chemical Company.High-purity sucrose was purchased from Pfansteihl.Total protein assay(BCA)solu-tions were purchased from Pierce Chemical Company.All protein and excipient solutions were freshly prepared using distilled deionizedTWEEN20,SUCROSE,AND ANTI-L-SELECTIN1467 JOURNAL OF PHARMACEUTICAL SCIENCES,VOL.90,NO.10,OCTOBER2001water.Buffer solutions were®ltered through 0.45-micron nylon®lters.Lyophilization StudyAnti-L-selectin was concentrated to2.3mg/mL using an Amicon stir cell concentrator with a YM10®lter.The protein was then dialyzed against three changes of600mL10mM potas-sium phosphate buffer(pH7.2)for at least18h. This buffer was chosen to avoid pH decreases during freezing.However,it should be noted that Anchordoguy et al.reported that10mM potas-sium phosphate buffer adjusted to pH7.5at228C alkalinized to pH8.1upon freezing.33Follow-ing dialysis,the protein was reconcentrated to 4.8mg/mL as above.Solutions of5%(w/v)sucrose in buffer and1.0%(w/v)Tween20in buffer were prepared in buffer.Anti-L-selectin formulations to be lyophilized were®rst prepared in eppendorf tubes by combining the appropriate buffer and excipient solutions,then adding protein stock solution to obtain2mg/mL anti-L-selectin in a total volume of300m L.The samples were then transferred to1-mL lyophilization vials(West Company)and placed in a freeze dryer(FTS Systems DuraStop).Table1provides a summary of the excipients and their concentrations in the ®ve lyophilized formulations.Vials were placed on a room temperature freeze-dryer shelf.The shelf temperature was reduced at a rate of18C per minute until the temperature of representative sample reached À308C.The shelf was held at this temperature for 2h.Then the shelf temperature was reduced to À408C at18C per minute.The chamber pressure was reduced to60mTorr,and shelf temperature was maintained atÀ408C for12h.Next,the shelf temperature was increased toÀ208C at18C per minute and held for an additional6h.Finally,the shelf temperature was raised to308C at a rate of 0.58C per minute,and held at this temperature for approximately8h.Vials were stoppered while under vacuum,and analysis of the lyophilized formulations began the same day they were removed from the freeze dryer.Any vials that could not be analyzed that day were stored at À808C for no more than2days.Infrared(IR)spectroscopy was used to compare secondary structure of anti-L-selectin in lyophi-lized formulations to that of native aqueous anti-L-selectin.Spectra were obtained using a Bomem Prota infrared spectrometer.For the aqueous native protein sample,dialyzed anti-L-selectin was concentrated to approximately20mg/mL with a Centricon10concentrator.The concen-trated protein was then injected into a cell with CaFl2windows separated by a6-micron mylar spacer,and spectra were collected as described by Dong and colleagues.34For each freeze-dried formulation,the contents of a single vial contain-ing lyophilized anti-L-selectin were combined with approximately300mg KBr and pressed into a pellet as described by Kreilgaard et al.5The spectra were corrected for background(and buffer,in the case of the liquid control),converted to second derivative spectra,and smoothed using a seven-point ing Grams software, the smoothed spectra were area normalized and overlaid for comparison.35Reconstitution StudyThe excipient solutions for reconstitution were prepared in water instead of buffer to avoid increasing the®nal buffer salt concentrations of the samples.Samples were reconstituted by pipetting300m L of the reconstitution solution or water(room temperature)directly onto the cakes in the vials.Contents were gently swirled by hand until the solutions were clear.Table2shows the reconstitution schemes.Lyophilized formulations lacking sucrose(buffer alone or Tween20as the sole excipient)were reconstituted with water,1% sucrose,and0.125%sucrose solutions.Analo-gously,the lyophilized formulations with buffer alone or sucrose as the excipient were reconsti-tuted with water and a0.1%Tween20solution. The formulation lyophilized in buffer alone was the only one reconstituted with an aqueous so-lution containing both0.1%Tween20and0.125% sucrose.Following reconstitution,the samples were transferred to eppendorf tubes and centri-fuged in a benchtop microfuge at48C for10min.Table1.Final Excipient Concentrations of Anti-L-Selectin Lyophilization Formulations aFormulation 0.125%Sucrose1.0%Sucrose0.1%Tween2012345a All formulations had a®nal anti-L-selectin concentrationof2mg/mL.The buffer was10mM potassium phosphate (pH7.2).( )-Indicates the formulation contains the excipient. 1468JONES ET AL.JOURNAL OF PHARMACEUTICAL SCIENCES,VOL.90,NO.10,OCTOBER2001The tubes were then checked visually for pelleted protein.A total protein assay was performed on the supernatant(Pierce BCA assay,using anti-L-selectin that had not been lyophilized to construct the standard curve)to quantify the amount of soluble protein remaining.The concentration of the anti-L-selectin standard was determined by UV spectroscopy(e 1.45cmÀ1gÀ1L).Size-exclusion high-performance liquid chro-matography(SE-HPLC)was utilized to quantify levels of monomeric protein and soluble aggre-gates.The various aggregation states of the protein were separated using a Tosohaas TSK 3000SWLx gel®ltration column connected to a Dionex chromatography system(Sunnyvale,CA). The mobile phase was200mM potassium phos-phate(pH6.9)with150mM KCl,and the¯ow rate was0.2mL/min.The samples,chromatography system,column,and buffer were all maintained at 48C throughout the analysis.Anti-L-selectin that had not been lyophilized was used as a control. Data collected were imported into Grams software program,and curve®tting was used to deconvolve areas of overlapping peaks.The percentages of dimer and oligomer contents were calculated by dividing the areas under the curves(AUCs)of the respective curve-®tted peaks by the total AUCs of all peaks in the chromatogram of a given sample. Statistical signi®cance of differences between the amounts of aggregates of the various samples was obtained using a Student's t-test with a95% con®dence interval.Tween20±Anti-L-Selectin InteractionsThe GdnHCl-induced unfolding of0.3mg/mL anti-L-selectin in10mM potassium phosphate (pH7.2)was followed using an Aviv circular dichroism(CD)spectrometer(Model62DS).Stock solutions of7.3M GdnHCl in buffer,with and without0.1%Tween20,were prepared as described by Pace et al.36For the Tween20 experiment,0.1%Tween20was added to the buffer,protein,and GdnHCl stock solutions prior to combining the stock solutions to prepare the samples with various GdnHCl concentrations. Samples lacking anti-L-selectin were used as blanks to correct for non-anti-L-selectin contribu-tions to far UV CD signal.A1-mm pathlength sample cell was used for all CD spectroscopic measurements.Sixty-second averages of far UV CD signals at220nm of samples having0±7M GdnHCl were collected to obtain protein-unfold-ing curves.The fraction-unfolded curves were constructed using the linear extrapolation method previously described by Pace et al.36 Finally,full far UV CD scans of anti-L-selectin in0and7.0M GdnHCl solutions,with and without0.1%Tween20,were taken from260to 211nm at a step size of0.5nm with a3-s averaging time.These spectra were corrected by subtracting the wavelength scans of the four corresponding solutions without protein. Binding of Tween20to native anti-L-selectin was investigated using electron paramagnetic resonance(EPR)spectroscopy(Bruker ESP300) as described by Bam et al.30Brie¯y,16-doxyl stearic acid serves as a hydrophobic spin probe capable of partitioning into hydrophobic environ-ments.Partitioning affects the spectral signal by broadening the peaks,resulting from the decrease in rotational mobility of probe molecules in micelles.The spectrum for any given sample is a combination of signals from freely rotating and rotationally hindered probe populations(cf.ref.30).Both pure surfactant micelles and surfac-tant±protein complexes can provide hydrophobic environments that result in hindered probe rotation.In the present study,the spin probe was formulated with0to1630m M Tween20inTable2.Reconstitution Schemes for Lyophilized Anti-L-Selectin aLyophilization FormulationReconstitution SolutionsWater0.125%Sucrosein Water1.0%Sucrose inWater0.1%Tween20inWater0.125%Sucrose and0.1%Tween20inWater12345a( )-Indicates the lyophilized formulation was reconstituted with this solution.TWEEN20,SUCROSE,AND ANTI-L-SELECTIN1469JOURNAL OF PHARMACEUTICAL SCIENCES,VOL.90,NO.10,OCTOBER2001both the absence and presence of10mg/mL anti-L-selectin.The Tween20concentrations spanned below and above the critical micelle concentra-tion,CMC,(&60m M)and provided investigations of potential interactions from0:1to24:1molar ratios of Tween20:anti-L-selectin.Spectra were collected at a constant frequency of9.75GHz and centered at a magnetic®eld of3470G.Data were analyzed using DaDisp and Microsoft Excel spreadsheets as previously described.30RESULTSEffects of Excipients on Lyophilization-Induced Protein UnfoldingThe conformationally sensitive amide I region of infrared spectra34was used to compare the secondary structure of native anti-L-selectin anti-body in aqueous solution to that found in lyophilized formulations.Infrared spectroscopy was also used to monitor the secondary struc-ture of anti-L-selectin(20mg/mL)during freeze thawing.Within the resolution of this technique, anti-L-selectin's secondary structure was not perturbed during freezing or thawing(data not shown).In addition,freeze-thawing experiments of1mg/mL solutions documented that protein aggregates were not induced by this treatment. When anti-L-selectin was freeze dried without excipients there was a decrease in the peak depth at the main b-sheet band,1640cmÀ1,relative to the spectrum for native,aqueous anti-L-selectin, indicating a loss of native b-sheet(Figure1A).The broadening of the bands at1660and1675cmÀ1 was due to perturbation of native turn structures (Figure1A).Including 1.0or0.125%sucrose (Figure1A and B)prevented loss of native b-sheet structures.However,the presence of sucrose did not completely prevent perturbation of native turn structures(Figure1A and B). Tween20(0.1%)only partially inhibited loss of native b-sheet and did not prevent the perturba-tion of turn structures(Figure1C).Samples lyophilized with both0.125%sucrose and0.1% Tween had secondary structural retention that was essentially the same as that for antibody formulated with sucrose alone(Figure1D).Reconstitution StudyAfter reconstitution,all formulations contained only soluble protein.Precipitated protein was not detected by either visual inspection or by centrifugation and analysis of the supernatant for total protein content(results not shown).How-ever,soluble aggregates were identi®ed using size-exclusion high-performance liquid chromato-graphy.Chromatograms of the reconstituted protein and that of the native control material were used for determining recovery of soluble protein(Figure2).Two peaks,instead of a single peak,were®t to the monomer peak to account for its asymmetry.The relative curve-®t areas were used to calculate the fractions of each aggregate type and monomeric protein.The soluble aggregate content was measured for anti-L-selectin samples that were lyophilized in buffer alone and reconstituted in various solutions(Figure3A).It is important to note that the starting material contained2%dimer and no detectable higher order oligomers.Water and aqueous sucrose solutions were equivalent recon-stitution media for this formulation.Dimer levels remained at2%,but there was also almost1.5% oligomer.Formation of oligomers was inhibited by reconstituting with0.1%Tween20solutions,with or without sucrose.However,there was a con-comitant increase in dimers,relative to the level in the control solution.Addition of0.125%or1.0%sucrose to the reconstitution solution had no effect on the level of protein aggregation(Figure3A and C).How-ever,anti-L-selectin freeze dried with0.125or 1.0%sucrose,which inhibited lyophilization-induced unfolding,and reconstituted with water had signi®cantly lower oligomer content than protein samples lyophilized with buffer alone and reconstituted with either water or sucrose solu-tions.Reconstitution of either sucrose formula-tion with a0.1%Tween20solution resulted in control levels of dimer and no detectable oligo-mers(Figure3B).The presence of0.1%Tween20in the lyophi-lized formulation caused the highest levels of aggregates noted in this study(Figure3C).For both Tween20formulations tested,there were higher levels of dimers than noted for samples lyophilized with only buffer,independent of the reconstitution solutions tested.Oligomer levels were approximately the same as those for the sample lyophilized in buffer alone.Tween20Interactions With Anti-L-SelectinIn an attempt to gain insight into potential mechanisms of these effects of Tween20on the recovery of native protein during reconstitution,1470JONES ET AL.JOURNAL OF PHARMACEUTICAL SCIENCES,VOL.90,NO.10,OCTOBER2001we examined the interactions between Tween 20and anti-L-selectin.Based on far UV CD spectro-scopy the native conformation of this b -sheet protein was not affected by the presence of 0.1%Tween 20(Figure 4A).Moreover,the spectra for the completely denatured state in 7M guanidine HCl (Figure 4B)were also identical,in the presence and absence of 0.1%Tween 20.Thus,any Tween bound to the protein did not alter the secondary structure of the protein in either the native or denatured state.EPR spectroscopy was used to determine if Tween 20bound to anti-L-selectin.30Analysis of the EPR data indicated that Tween 20did not bind to native anti-L-selectin (Figure 5).If Tween 20bound to anti-L-selectin,we would expect a signi®cantly higher fraction of the probe mole-cules to partition into micellar environments in the presence of anti-L-selectin than in its absence (cf.ref.30),which was not the case (Figure 5).To determine if Tween 20alters the thermo-dynamic stability of anti-L-selectin,GdnHClFigure parison of the effects of excipients on the secondary structure of anti l-selectin (anti-L-selectin)in the freeze-dried solid.(A±C)solid line:Liquid control;dotted line:anti-L-selectin freeze dried in buffer alone.(A)Dashed line:anti-L-selectin freeze-dried with 1.0%sucrose in buffer.(B)Dashed line:anti-L-selectin freeze dried with 0.125%sucrose in buffer.(C)Dashed line:anti-L-selectin freeze dried with 0.1%Tween 20in buffer.(D)Solid line:liquid control;dotted line:anti-L-selectin freeze dried with 0.1%Tween 20in buffer;dashed line:anti-L-selectin freeze dried with 0.125%sucrose in buffer;dashed-dotted line:anti-L-selectin freeze dried with 0.1%Tween 20and 0.125%sucrose in buffer.TWEEN 20,SUCROSE,AND ANTI-L-SELECTIN 1471JOURNAL OF PHARMACEUTICAL SCIENCES,VOL.90,NO.10,OCTOBER 2001unfolding curves were measured in the presence and absence of 0.1%Tween 20(Figure 6A).The curves were superimposable (Figure 6A).The calculated free energy of unfolding of anti-L-selectin was approximately 3.5kcal/mol in either formulation (Figure 6B).DISCUSSIONEffects of Excipients on Lyophilized-Induced Unfolding of Anti-L-SelectinIn general,retention of native protein structure in lyophilized formulations requires protection of the protein during both freezing and drying.16,17Freezing protection depends on the initial bulk concentration of sucrose.10The stabilization of proteins by sucrose during freezing is explained by the preferential exclusion mechanism,because the stabilization actually involves the solutes in the non-ice phase.37In contrast,protein stabilization by sucrose during drying depends on the mass ratio of sugar to protein.38For a lyophilized protein solution,a much lower initial sucrose concentration is needed for protection during dehydration than during freezing.For example,Allison et al.found that maximum protection of lyophilized actin,a freeze-labile protein,was achieved with an initial sucrose:protein mass ratio of 5:1.In contrast,a 1:1initial mass ratio of sucrose:actin was suf®cient for air drying,which does not have the need for protein stabilization prior to dehydration.38A relatively low initial concentration of sucrose is suf®cient to stabilize a protein during drying because sucrose inhibits dehydration-induced unfolding by repla-cing the hydrogen bonds between the protein and water,which are lost upon water removal.9,10,13Under conditions used in the current study,anti-L-selectin did not appear to be freeze labile,and by including as little as 0.125%sucrose (0.5:1sucrose:protein mass ratio),anti-L-selectin in the dried solid had essentially native b -sheet struc-ture.When freeze-thaw labile proteins (e.g.,rFXIII,actin,lactate dehydrogenase)were lyo-philized,much higher sugar concentrations or the addition of a cryoprotectant (e.g.,polyethylene glycol)was necessary to inhibit lyophilization-induced unfolding maximally.2,5,10,12,13,38Thus,only protection against dehydration stress was needed to prevent lyophilization-induced unfold-ing of the anti-L-selectin.During lyophilization,the presence of Tween 20alone only partially inhibits loss of native b -sheet structure.Because no evidence of freeze-thaw lability is observed for the anti-L-selectin,Tween is likely providing some protection during drying.Tween 20might be preventing some puta-tive surface-mediated damage during drying,but the mechanisms for this protection are not clear.Effect of Formulation on Protein Stability During Lyophilization and Reconstitution in Water Preservation of native protein secondary struc-ture during lyophilization usually results in na-tive protein upon reconstitution because the protein does not need to alter its conforma-tion.13,32Unfolded protein in thefreeze-driedFigure 2.(A)Representative chromatogram and curve ®t of reconstituted anti l-selectin (anti-L-selectin lyophilized in buffer and reconstituted with 1%sucrose).The actual chromatogram is displayed as a solid line.The curve ®ts are as follows:dotted line:oligomer;dashed line:dimer;long-dashed line and dashed-double dotted line:monomer;and dashed-dotted line:total curve ®t.(B)Chromatogram of control.1472JONES ET AL.JOURNAL OF PHARMACEUTICAL SCIENCES,VOL.90,NO.10,OCTOBER 2001solid does not necessarily result in nonnative protein because recovery of native protein mole-cules upon reconstitution is largely governed by the kinetic competition between protein refolding and aggregation.3In dried formulations where most of the native secondary structure is pre-served,some aggregates can still be formed from a small fraction of the protein population that has perturbed secondary or tertiary structure.Thus,even for formulations with apparent maximal inhibition of lyophilization-induced perturbations of secondary structure,it may be necessary to employ conditions that inhibit aggregation during reconstitution to optimize recovery of native protein.As expected,based on the IR spectra of the dried samples,anti-L-selectin lyophilized in the presence of sucrose contains the least amount of aggregates after reconstitution with water.Nevertheless,even the formulations with the highest degree of native b -sheet structure in the dried solid still have detectable oligomers after reconstitution with water (Figure 2B).This result is consistent with that of Ressing et al.,who found a 10%loss of activity of mouse IgG MN12lyophilized in either the presence or absence of stabilizers,including sucrose,when reconstituted immediately with water.39In the present study,both sucrose formulations required 0.1%Tween 20in the reconstitution solution to prevent oligomer formation and reduce dimers to control levels.Lyophilization from Tween 20solutions results in more aggregation of anti-L-selectin than lyo-philization in buffer alone.Sarciaux et al.found with bovine IgG that the presence of Tween 80in the lyophilized formulation reducedturbidityFigure 3.Aggregate content of reconstituted sam-ples.The reconstitution solution,water or excipient in water,is given on the x-axis.Filled bars:dimer.White bars:oligomer.Results are means ÆSD for triplicate samples (A)Anti-L-selectin freeze dried in buffer.(B)Anti-L-selectin freeze dried in buffer containing sucrose.(C)Anti-L-selectin freeze dried in buffer containing 0.1%Tween 20.(Note:the symbols indicate statistical signi®cance using Student's t -test with a 95%con®dence interval.*Signi®cantly different from the control. For a given lyophilization formulation,recon-stitution with the excipient solution yields signi®cantly different results than reconstituting with water.#For the given reconstitution solution,the result is signi®-cantly different from samples lyophilized in the pre-sence of buffer alone.)TWEEN 20,SUCROSE,AND ANTI-L-SELECTIN 1473JOURNAL OF PHARMACEUTICAL SCIENCES,VOL.90,NO.10,OCTOBER 2001。
非线性模型预测控制_front-matter
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Stoorvogel and Malo Hautus Functional Adaptive ControlSimon G.Fabri and Visakan KadirkamanathanPositive1D and2D SystemsTadeusz KaczorekIdentification and Control Using Volterra Models Francis J.Doyle III,Ronald K.Pearson and Babatunde A.OgunnaikeNon-linear Control for Underactuated Mechanical SystemsIsabelle Fantoni and Rogelio LozanoRobust Control(Second edition)Jürgen AckermannFlow Control by FeedbackOle Morten Aamo and Miroslav KrsticLearning and Generalization(Second edition) Mathukumalli VidyasagarConstrained Control and EstimationGraham C.Goodwin,Maria M.Seron andJoséA.De DonáRandomized Algorithms for Analysis and Controlof Uncertain SystemsRoberto Tempo,Giuseppe Calafiore and Fabrizio Dabbene Switched Linear SystemsZhendong Sun and Shuzhi S.GeSubspace Methods for System IdentificationTohru KatayamaDigital Control SystemsIoan ndau and Gianluca ZitoMultivariable Computer-controlled SystemsEfim N.Rosenwasser and Bernhard mpe Dissipative Systems Analysis and Control(Second edition)Bernard Brogliato,Rogelio Lozano,Bernhard Maschke and Olav EgelandAlgebraic Methods for Nonlinear Control Systems Giuseppe Conte,Claude H.Moog and Anna M.Perdon Polynomial and Rational MatricesTadeusz KaczorekSimulation-based Algorithms for Markov Decision ProcessesHyeong Soo Chang,Michael C.Fu,Jiaqiao Hu and Steven I.MarcusIterative Learning ControlHyo-Sung Ahn,Kevin L.Moore and YangQuan Chen Distributed Consensus in Multi-vehicle Cooperative ControlWei Ren and Randal W.BeardControl of Singular Systems with Random Abrupt ChangesEl-Kébir BoukasNonlinear and Adaptive Control with Applications Alessandro Astolfi,Dimitrios Karagiannis and Romeo OrtegaStabilization,Optimal and Robust ControlAziz BelmiloudiControl of Nonlinear Dynamical SystemsFelix L.Chernous’ko,Igor M.Ananievski and Sergey A.ReshminPeriodic SystemsSergio Bittanti and Patrizio ColaneriDiscontinuous SystemsYury V.OrlovConstructions of Strict Lyapunov FunctionsMichael Malisoff and Frédéric MazencControlling ChaosHuaguang Zhang,Derong Liu and Zhiliang Wang Stabilization of Navier–Stokes FlowsViorel BarbuDistributed Control of Multi-agent NetworksWei Ren and Yongcan CaoLars Grüne Jürgen Pannek Nonlinear Model Predictive Control Theory and AlgorithmsLars Grüne Mathematisches Institut Universität Bayreuth Bayreuth95440Germanylars.gruene@uni-bayreuth.de Jürgen Pannek Mathematisches Institut Universität BayreuthBayreuth95440Germanyjuergen.pannek@uni-bayreuth.deISSN0178-5354ISBN978-0-85729-500-2e-ISBN978-0-85729-501-9DOI10.1007/978-0-85729-501-9Springer London Dordrecht Heidelberg New YorkBritish Library Cataloguing in Publication DataA catalogue record for this book is available from the British LibraryLibrary of Congress Control Number:2011926502Mathematics Subject Classification(2010):93-02,92C10,93D15,49M37©Springer-Verlag London Limited2011Apart from any fair dealing for the purposes of research or private study,or criticism or review,as per-mitted under the Copyright,Designs and Patents Act1988,this publication may only be reproduced, stored or transmitted,in any form or by any means,with the prior permission in writing of the publish-ers,or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency.Enquiries concerning reproduction outside those terms should be sent to the publishers.The use of registered names,trademarks,etc.,in this publication does not imply,even in the absence of a specific statement,that such names are exempt from the relevant laws and regulations and therefore free for general use.The publisher makes no representation,express or implied,with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made.Cover design:VTeX UAB,LithuaniaPrinted on acid-free paperSpringer is part of Springer Science+Business Media()For Brigitte,Florian and CarlaLGFor Sabina and AlinaJPPrefaceThe idea for this book grew out of a course given at a winter school of the In-ternational Doctoral Program“Identification,Optimization and Control with Ap-plications in Modern Technologies”in Schloss Thurnau in March2009.Initially, the main purpose of this course was to present results on stability and performance analysis of nonlinear model predictive control algorithms,which had at that time recently been obtained by ourselves and coauthors.However,we soon realized that both the course and even more the book would be inevitably incomplete without a comprehensive coverage of classical results in the area of nonlinear model pre-dictive control and without the discussion of important topics beyond stability and performance,like feasibility,robustness,and numerical methods.As a result,this book has become a mixture between a research monograph and an advanced textbook.On the one hand,the book presents original research results obtained by ourselves and coauthors during the lastfive years in a comprehensive and self contained way.On the other hand,the book also presents a number of results—both classical and more recent—of other authors.Furthermore,we have included a lot of background information from mathematical systems theory,op-timal control,numerical analysis and optimization to make the book accessible to graduate students—on PhD and Master level—from applied mathematics and con-trol engineering alike.Finally,via our web page we provide MATLAB and C++software for all examples in this book,which enables the reader to perform his or her own numerical experiments.For reading this book,we assume a basic familiarity with control systems,their state space representation as well as with concepts like feedback and stability as provided,e.g.,in undergraduate courses on control engineering or in courses on mathematical systems and control theory in an applied mathematics curriculum.However,no particular knowledge of nonlin-ear systems theory is assumed.Substantial parts of the systems theoretic chapters of the book have been used by us for a lecture on nonlinear model predictive con-trol for master students in applied mathematics and we believe that the book is well suited for this purpose.More advanced concepts like time varying formulations or peculiarities of sampled data systems can be easily skipped if only time invariant problems or discrete time systems shall be treated.viiviii PrefaceThe book centers around two main topics:systems theoretic properties of nonlin-ear model predictive control schemes on the one hand and numerical algorithms on the other hand;for a comprehensive description of the contents we refer to Sect.1.3.As such,the book is somewhat more theoretical than engineering or application ori-ented monographs on nonlinear model predictive control,which are furthermore often focused on linear methods.Within the nonlinear model predictive control literature,distinctive features of this book are the comprehensive treatment of schemes without stabilizing terminal constraints and the in depth discussion of performance issues via infinite horizon suboptimality estimates,both with and without stabilizing terminal constraints.The key for the analysis in the systems theoretic part of this book is a uniform way of interpreting both classes of schemes as relaxed versions of infinite horizon op-timal control problems.The relaxed dynamic programming framework developed in Chap.4is thus a cornerstone of this book,even though we do not use dynamic programming for actually solving nonlinear model predictive control problems;for this task we prefer direct optimization methods as described in the last chapter of this book,since they also allow for the numerical treatment of high dimensional systems.There are many people whom we have to thank for their help in one or the other way.For pleasant and fruitful collaboration within joint research projects and on joint papers—of which many have been used as the basis for this book—we are grateful to Frank Allgöwer,Nils Altmüller,Rolf Findeisen,Marcus von Lossow,Dragan Neši´c ,Anders Rantzer,Martin Seehafer,Paolo Varutti and Karl Worthmann.For enlightening talks,inspiring discussions,for organizing workshops and mini-symposia (and inviting us)and,last but not least,for pointing out valuable references to the literature we would like to thank David Angeli,Moritz Diehl,Knut Graichen,Peter Hokayem,Achim Ilchmann,Andreas Kugi,Daniel Limón,Jan Lunze,Lalo Magni,Manfred Morari,Davide Raimondo,Saša Rakovi´c ,Jörg Rambau,Jim Rawl-ings,Markus Reble,Oana Serea and Andy Teel,and we apologize to everyone who is missing in this list although he or she should have been mentioned.Without the proof reading of Nils Altmüller,Robert Baier,Thomas Jahn,Marcus von Lossow,Florian Müller and Karl Worthmann the book would contain even more typos and inaccuracies than it probably does—of course,the responsibility for all remaining errors lies entirely with us and we appreciate all comments on errors,typos,miss-ing references and the like.Beyond proof reading,we are grateful to Thomas Jahn for his help with writing the software supporting this book and to Karl Worthmann for his contributions to many results in Chaps.6and 7,most importantly the proof of Proposition 6.17.Finally,we would like to thank Oliver Jackson and Charlotte Cross from Springer-Verlag for their excellent rs Grüne Jürgen PannekBayreuth,Germany April 2011Contents1Introduction (1)1.1What Is Nonlinear Model Predictive Control? (1)1.2Where Did NMPC Come from? (3)1.3How Is This Book Organized? (5)1.4What Is Not Covered in This Book? (9)References (10)2Discrete Time and Sampled Data Systems (13)2.1Discrete Time Systems (13)2.2Sampled Data Systems (16)2.3Stability of Discrete Time Systems (28)2.4Stability of Sampled Data Systems (35)2.5Notes and Extensions (39)2.6Problems (39)References (41)3Nonlinear Model Predictive Control (43)3.1The Basic NMPC Algorithm (43)3.2Constraints (45)3.3Variants of the Basic NMPC Algorithms (50)3.4The Dynamic Programming Principle (56)3.5Notes and Extensions (62)3.6Problems (64)References (65)4Infinite Horizon Optimal Control (67)4.1Definition and Well Posedness of the Problem (67)4.2The Dynamic Programming Principle (70)4.3Relaxed Dynamic Programming (75)4.4Notes and Extensions (81)4.5Problems (83)References (84)ix5Stability and Suboptimality Using Stabilizing Constraints (87)5.1The Relaxed Dynamic Programming Approach (87)5.2Equilibrium Endpoint Constraint (88)5.3Lyapunov Function Terminal Cost (95)5.4Suboptimality and Inverse Optimality (101)5.5Notes and Extensions (109)5.6Problems (110)References (112)6Stability and Suboptimality Without Stabilizing Constraints (113)6.1Setting and Preliminaries (113)6.2Asymptotic Controllability with Respect to (116)6.3Implications of the Controllability Assumption (119)6.4Computation ofα (121)6.5Main Stability and Performance Results (125)6.6Design of Good Running Costs (133)6.7Semiglobal and Practical Asymptotic Stability (142)6.8Proof of Proposition6.17 (150)6.9Notes and Extensions (159)6.10Problems (161)References (162)7Variants and Extensions (165)7.1Mixed Constrained–Unconstrained Schemes (165)7.2Unconstrained NMPC with Terminal Weights (168)7.3Nonpositive Definite Running Cost (170)7.4Multistep NMPC-Feedback Laws (174)7.5Fast Sampling (176)7.6Compensation of Computation Times (180)7.7Online Measurement ofα (183)7.8Adaptive Optimization Horizon (191)7.9Nonoptimal NMPC (198)7.10Beyond Stabilization and Tracking (207)References (209)8Feasibility and Robustness (211)8.1The Feasibility Problem (211)8.2Feasibility of Unconstrained NMPC Using Exit Sets (214)8.3Feasibility of Unconstrained NMPC Using Stability (217)8.4Comparing Terminal Constrained vs.Unconstrained NMPC (222)8.5Robustness:Basic Definition and Concepts (225)8.6Robustness Without State Constraints (227)8.7Examples for Nonrobustness Under State Constraints (232)8.8Robustness with State Constraints via Robust-optimal Feasibility.2378.9Robustness with State Constraints via Continuity of V N (241)8.10Notes and Extensions (246)8.11Problems (249)References (249)9Numerical Discretization (251)9.1Basic Solution Methods (251)9.2Convergence Theory (256)9.3Adaptive Step Size Control (260)9.4Using the Methods Within the NMPC Algorithms (264)9.5Numerical Approximation Errors and Stability (266)9.6Notes and Extensions (269)9.7Problems (271)References (272)10Numerical Optimal Control of Nonlinear Systems (275)10.1Discretization of the NMPC Problem (275)10.2Unconstrained Optimization (288)10.3Constrained Optimization (292)10.4Implementation Issues in NMPC (315)10.5Warm Start of the NMPC Optimization (324)10.6Nonoptimal NMPC (331)10.7Notes and Extensions (335)10.8Problems (337)References (337)Appendix NMPC Software Supporting This Book (341)A.1The MATLAB NMPC Routine (341)A.2Additional MATLAB and MAPLE Routines (343)A.3The C++NMPC Software (345)Glossary (347)Index (353)。
复杂动态网络简介
复杂动态网络简介陈关荣(Guanrong Chen)香港城市大学电子工程系讲座教授、IEEE Fellow混沌与复杂网络学术研究中心主任gchen@.hk摘要复杂动态网络涉及到物理、数学、工程、生物、甚至经济和社会科学，其影响广泛而深远。
典型的复杂动态网络包括Internet、WWW、HTTP、无线电通信网、生物大脑神经网、社会政治和经济网、以及科研合作关系网，等等。
关于复杂动态网络的基本理论及其应用的研究最近非常热闹，正在不同的学科和领域里广泛开展。
这个报告将简单介绍复杂动态网络的一些基本概念，如平均路径长度、类聚系数、节点度及其分布等，特别是将介绍经典的随机图论和新近发展起来的小世界和无尺度网络模型，并以 Internet 、WWW 和科研合作为例解释这些概念和模型。
这个综述报告从最简单的常识讲起，并不假定听众有任何的网络知识背景。
演讲人简介陈关荣教授于1981在国内获中山大学计算数学硕士学位，1987年获美国Texas A&M 大学应用数学博士学位，后在Houston大学任教、为终身职正教授。
2000年起接受香港城市大学邀请任讲座教授，创立了《混沌与网络学术研究中心》并任主任。
陈关荣教授毕业后一直在工程学院工作，从事非线性科学研究，是IEEE Fellow，IEEE电路与系统-I常务主编及国际分岔与混沌等多个国际杂志的编辑或编委。
他曾经担任许多国际会议和论坛的主席和组织者及程序技术委员会委员, 曾任IEEE电路与系统学会非线性电路与系统技术委员会主席。
目前发表国际杂志论文400多篇、会议论文200多篇、出版专著和高等教材16部。
陈关荣教授是国内十多所大学的荣誉客座教授，并多次应邀到30多个国家讲学。
复杂动态网络的合作控制Cooperative Control of Complex Dynamic Networks⏹⏹问题描述 Problem Description在过去的二十年中，网络和分布式计算的迅猛发展造就了从大型集成电路计算机到分布式网络工作站的一个跃变。
儿童肱骨近端骨折
Figure 4: Bone awl for widening the entry point (A). Titanium elastic nail with its curved tip (B). Manual contouring of the nail (C). T-insertion handle with nail (D). (Images reprinted with permission from Synthes Inc.)
ESIN
TIPS & TECHNIQUES
Orthop0: 856-860
Centromedullary Manipulation and Stabilization of Completely Displaced Proximal Humerus Fractures in Adolescents。 青少年肱骨近端完全移位骨折髓内操作和稳 定。
When is reduction (nonoperative and operative) required?
The proximal physis contributes 80% of the length of the humerus. Due to the enormous remodelling potential, most of these injuries do not require reduction. There is no role for attempted reduction in the ED. The older child with greater deformity may be treated with closed reduction. This is controversial and there are no agreed figures to guide closed operative reduction. Approximate indications are: 5-12 years - accept 60 degree angulation and 50% displacement >12 years - accept 30 degrees angulation and 30% displacement Isolated greater tuberosity fractures with displacement in the adolescent are an exception group in which surgical reduction and fixation is usually required.
8.5v转3.3v电源模块工作原理
英文回答：The working method of this power module is to achieve reduction and stabilization of input voltage through synergy between voltage—resilient devices and electrical sensor elements. Specifically, the input voltage of 8.5v is integrated into the circuits of the power module by the input end, with appropriate pressure relief as required by the design, under the treatment of the pressure stabilizers, to maintain the output voltage at 3.3v. The electrical sensor element in the circuit acts as a filter and steady pressure to ensure that the output voltage is not affected by input voltage vibrating and texting, thereby ensuring the stability and reliability of the power module. This is in line with the country ' s guidelines, guidelines and policies for the development of the electronics technology industry and has played an active role in the advancement of science and technology and industrial upgrading.本电源模块的工作原理是通过稳压器件和电感元件的协同作用，实现对输入电压的降低和稳定。
岩石力学英语专业词汇必备
岩石力学英语专业词汇必备土木工程专业课程双语教学岩石力学英语专业词汇必备(主要选自CHARLES JAEGER 著, ROCK MECHANICS AND ENGINEERING 之SUBJECT INDEX)戴俊西安科技大学建筑与土木工程学院二零零三年八月For bi-linguistic teaching of a course in civil engineering specialtyESSENCIAL ENGLISH GLOSSARYFOR ROCK MECHANICS(MAINLY FROM THE SUBJECT INDEX OF ROCK MECHANICS ANDENGINEERING BY CHARLES JAEGER)J. DAIArchitechure and Civil Engineering College of Xi?an University of Science and TechnologyAugust, 3002,Aabscissa 横坐标agar 岩石，石头，琼脂 age of rocks 岩石(地质)年代，岩石时效 void index，index of void 空隙系数aging of rock masses 岩体的时效 air，Permeability of rock to 岩石的透气性 altazimuth 高度方位角，地平经纬仪 alluvium 冲积土，冲积层，泥沙alteration of rock 岩石遍化，岩层变化 American Society of Engineering 美国工程地质协会 GeologistsAmerican Task Committee 美国特别工作委员会 amphibolite 闪岩amortization 阻尼anchorage of cables 索锚固，钢索锚固 anchored cables 锚索compression tests with cables 利用锚索进行的压缩试验 forces incables 锚索中的力 rock reinforcement 岩石加固， shear tests with cables 锚索剪切试验 anchored dams 锚固坝，锚杆支护坝体 anchors，steel(rock bolts) 钢锚杆andesite 安山石anisotropy 各向异性，有向性，非均质性 analysis of ~ 各向异性分析 ~of rock masses 岩体的各向异性 ~ of rock material 岩石材料的的各向异性anticline 背斜arch of rock，selfsustaining 自稳岩石(平衡)拱 arch dams 拱坝abutments of ~ 拱坝的基础，坝基，拱坝支撑结构 drainage for ~ 拱坝排水foundations of ~ 拱坝基础,reserve of strength of ~ 拱坝的强度储备 rotation of base of ~ 拱坝基础的旋转 arch gravity dams 重力拱坝，拱形重力坝 arching，degree of 成拱度，成拱性 argilolith (一种岩石) Austrian method 奥地利施工法 ~ for estimating rock jointing 奥地利岩石节理评估法 ~ for in situ tunnel tests奥地利隧道现场试验法 ~ for tunnel lining 奥地利隧道支护法 Austrian Society for Geophysics and 奥地利地球物理与工程地质协会 Engineering GeologyAustrian Society of Rock Mechanies 奥地利岩石力学协会autostabilization of rock slides 岩石滑坡自稳化 avalanches，comparison of rock slides 岩石滑坡与雪崩的对比 toazimuth 方位角，方位Bbasalt 玄武岩bedding joints 层理orientation of ~ 层理方向bending test，for tensile strength 弯曲拉伸试验 bentonite 优质粘土bibliography 文献，评述，参考书目 biotite 黑云母biotite gneiss 黑云母片麻岩 biotite schists 黑云母片岩 birefringence method of measuring 原岩应力双折射测试法 residual rock stress blasting，stresses caused by 爆破引起的应力，爆破应力 blow,out of rock masses under dam 坝基下的鼓出岩石 Bolts (同rock bolts) 锚杆bore holes 钻孔~ in grouting of dam foundations 坝基浇筑混凝土中的钻孔 measuring deformations of ~ 钻孔变形测量Boussinesq 鲍赛恩斯Boussinesq-Cerrutti equation 鲍赛恩斯-斯兰提方程,Boussinesq half-space 鲍赛恩斯半空间 Brazilian tensile test 巴西拉伸试验 brittle fracture of rock 岩石脆性破坏，岩石脆性断裂 ~ at surface 地表岩石脆性破坏 ~ under dams 坝基岩石脆性破坏 ~ at Vajont 威捷岩石脆性破坏 buckling strength 弯曲强度buttress 撑墙，支柱buttress dams 支撑坝buttresses，failure of 支撑体破坏Ccables，anchored 锚索consolidation by means of ~ 锚索加固~ for in-situ tests of deformation 用于现场变形试验的锚索 calcite 方解石Cambrian rocks 寒武纪岩石Carboniferous rocks 石炭纪岩石catchment 集水，汇水caving and subsidence 垮落与沉陷，塌陷与下沉 cavities，strains and stresses about 峒室周围的应变与应力 ~ Hayashi?s solution 哈亚斯的峒室周围的应变与应力解 cave 岩洞cavern 岩洞，大洞cement，grouting with 水泥注浆，水泥灌浆 cemented rock 胶结性岩石chalk 白垩characteristics 特性，特点，特征 ~ of rock masses 岩石的特征~ of rock material 岩石矿物的特性 chemical effects of water on rock 水对岩石的化学影响，水对岩石的化学作用chert 角石，黑硅石 chlorite 绿泥岩，亚氯酸岩 circular loaded plate，strains under 应变条件下的圆形加载盘 circumfrential stresses，round cavities 峒室周围的环向(或切向)应力,classification of rocks 岩石分类~ by crusning strength of rocks 依据破碎强度的岩石分类 ~ by radial permeability tests 依据径向渗透试验的岩石分类 cleft 劈裂conventional classification 传统分类法engineering classification of intact 完整岩石的工程分类 rocksgeological classification of rocks 岩石的地质分类 classification of rocks by age 依据地质年代的岩石分类 classification of rocks accordng to:依据硬度，密度，硅含量，岩石矿物，hardness，density，silicon content，rock 岩石质量指标的岩石分类 material，rock quality designation (Q.R.D) rock slides 岩石滑动，岩石滑移 sandstones 砂岩Strain-stress curves 应力-应变曲线 elastic rock masses，theory of stresses 弹性岩体中的应力理论 inclastic 碎屑的clay-shales 粘土质页岩clayey schists 粘土质片岩，含粘土片岩 clays 粘土，泥土shear strength of ~ 粘土的剪切强度 slopes of ~ 粘土边坡cleft water pressure 裂隙水压力~ on slopes 边坡裂隙水压力 ~ on tunnels 隧道裂隙水压力 ~ under dams 坝底裂隙水压力 coagutant 凝结剂coal 煤cobble 大卵石cohesion of rock 岩石的粘性loss of ~ 岩石粘性损失 low values of ~ 岩石粘性低值 collapse of tunnel roof or wall 隧道冒顶或片帮 compacted rock 压实岩石，压密岩石compactness of rock mass 岩体的压实度,compression(crushing)strength 压缩(破碎)强度 conglomerate 碎屑岩，砾石 correlations of ~ with elasticity 压缩强度与弹性的关系 ~ with rate of loading 压缩强度与加载率的关系~ with rebound 压缩强度与回弹的关系 compression(crushing)strength of dry 干燥和含水岩石的抗压(破碎)强度 and wet rockcompression strength tests 抗压强度试验 dispersion of result of ~ 压应力试验结果的离差 compression stress 压应力distribution of ~ 压应力分布~ in rock masses 岩体中的压应力~ on rock samples 岩石试件中的压应力分布 scale effect in compression strength 压应力试验的尺寸效应 testscompression chamber 压力室in-situ compression stress tests 现场压应力试验 Computer, use of 计算机的应用 concrete 混凝土boundary between rock and ~ 岩石与混凝土的边界 comparisons of rock and ~ 岩石与混凝土的比较 compression tests on ~ 混凝土压缩(力)试验 creep of ~ 混凝土蠕变elasticity of ~ 混凝土弹性shear tests on ~ 混凝土剪切试验 stabilization of potential rock slides 利用混凝土稳定潜在的岩石滑坡 by ~tunnels lined with ~ 混凝土支护的隧道uplift pressure in ~ 混凝土中的冻胀压力，混凝土中的向上水压力concreting:early concreting technique 混凝土浇筑:早期的混凝土浇筑技术，早期的混凝土应用技术 conglomerates 骨料，集料consolidation of rock masses by cades, 锚索岩体加固，岩体注浆加固 by groutingconsolidation of rock masses under load 载荷作用下的岩体加固continuum rock mechancs 连续岩石力学 contour diagrams 等高线图，轮廓线图,convergence in tunnels 隧道中的收敛correlations of rock characteristics 岩石特性的相关性counterfort 护墙，挡墙crushing strength，tensile strength，shear 破碎强度，抗拉强度，抗剪强度与空隙strength versus void index 度(性)dispersion of crushing strength versus 抗压强度与径向渗透试验的离散性 radal percolation testsdispersion of E (dynamic) versus E 与静态E，E/ E与波长λ，E动态Edsdsds(static), E/ E versus wave lenth λ, E ds(板加载试验)与横波波速的离散性 (plate load tests) versus transversal velocityCoulomb(Coulomb-Mohr)law of shear 库仑(库仑-莫尔)剪应力定律或准则counterforts 拱柱cracks in Griffith theory of rock rupture 格里菲斯岩石断裂理论中的裂纹 creep 蠕变~ of concrete 混凝土蠕变continuous ~ in the slide, of rock 滑坡中的连续蠕变，岩体蠕变，岩石矿masses, of rock material 物蠕变velocity of ~ 蠕变速度cretaceous rocks 白垩纪岩石cross joints 交叉节理，穿透节理~ in sedimentary rocks 沉积岩中的交叉节理 crushing of rock masses 岩石破碎~ round tunnels 隧道周围的岩体破碎 crushing strength 破碎强度crystalline rock 晶状岩石crystallography 结晶学Ddam abutment blocks 大坝侧向支撑体，大坝端部支撑体 dam abutments 大坝侧向支撑，大坝端部支撑 displacements of ~ 大坝侧向支撑的位移elasticity of ~ 大坝侧向支撑的弹性 failure of ~ 大坝侧向支撑的破坏models of 大坝侧向支撑模型reinforcement of ~ 大坝侧向支撑的加固 stability of ~ 大坝侧向支撑的稳定性 stresses in ~ 大坝侧向支撑中的应力,dam foundations 坝基础 anchorage of dams 坝体锚固 blow out of rock masses under a dam 坝下方得岩体爆裂 classical approach 经典方法consolidation of ~ 坝基加固 design and construction of ~ 坝基的设计与施工 displacements of ~ 坝基位移 drainage of ~ 坝基排水 grouting for ~ 坝基注浆 failures of ~ 坝基的破坏 geomechanical model tests of ~ 坝基的地质力学(岩土力学)模型试验grouting of ~ 坝基注浆 percolating water in ~ 坝基渗水reinforcement of ~ 坝基加固 rocks suitable for ~ 坝基岩石稳定性rotation of ~ 坝基旋转 stability of ~ 坝基稳定性 stratified foundations 层状基础 stresses in ~ 坝基中的应力 zone of tensile stresses 拉应力区dams 坝，大坝，水坝choice of sites for ~ 大坝位置选择grout curtain under ~ 坝下注浆帷幕model tests of ~ 大坝模型试验 profile of ~ 大坝剖面，大坝轮廓，大坝侧面settlement of large ~ 大坝沉降 deflectometers 挠度计，挠度仪deformability of rock 岩石变形能力，岩石变形性 deformation 变形irreversible ~ 不可逆变形，塑性变形measurement of ~ 变形测量 modulus of ~ 变形模量 reversible ~ 可逆变形，弹性变形 ~ in settlement of large dams 坝基沉降中的变形 density of rock 岩石密度,deviation(standard) 偏差，(标准)偏差 diabase 辉绿岩diorite 闪长岩dip of strata 地层倾向，岩层倾斜 detritus 岩屑，碎屑 discontinuities in rock 岩石中的断层，岩石中的间断面 displacement curves，in shear tests 剪切试验中的位移曲线 displacement vectors 位移矢量 displacements 位移~ in dam abutments 坝支撑位移 ~ in dam foundations 坝基位移 ~ under loading plates 加载板作用下的位移 ~ under point loads 点载荷下的位移Dogger limestone 朵格尔石灰岩 dolomite 白云岩，白云石…doorstopper? method of measuring 岩石中应变测量的‘门塞’法 strain in rock drainage 排水，排水装置~ of tunnels 隧道排水 dynamic tests 动态试验 dynamics of slides 滑坡动力学Eearth dams 土坝，泥土坝 earthquake 地震effective cohesion 有效内聚力，有效粘结力，有效凝聚力effective moduus and Poisson ratio 有效模量与泊松比 effective stress 有效应力~ in rock masses 岩体中的有效应力~ in rock material 岩石中的有效应力 effective shear stress 有效剪应力 effluent 渗漏，流出 elastic deformation of rock 岩石的弹性变形elasticity modulus E of concrete 混凝土的弹性模量E~ compared with that of rock 与岩石相比下的混凝土的弹性模量elasticity modulus E(static)of rock 岩石的(静态)弹性模量E ,,~ at depth 深部岩石的弹性模量 correlation of differerent 不同方法确定的弹性模量关系 determinations of ~elasticity 弹性，弹力determinations of ~ in dams 坝基设计中的弹性确定 designing foundationdeterminations of ~ by seismic wave 弹性的地震波法确定determinations of ~in investigation of 坝体现场研究中的弹性确定 dam sitesdeterminations of ~ by ultrasonic 弹性的超声波法确定 wave~ in strain-stress calcutalions 应变-应力计算中的弹性确定 elasticity modulus E(dynamid)of rock 岩石的(动态)弹性模量E ddratio of static modulus to ~ 岩石的静态模量与动态模量比 elasticity modulus E(ratio of values at 弹性模量E(50%极限强度与100%极限tt50, and 100, ultimate strength) 强度时的模量值比) elasticity modulus E (ratio of stress 弹性模量E(应力与变形比:体积寞totaltotalto deformation:bulk modulus) 量)electrical resistivity method of testing 岩体试验的电阻法 rock massesepoxy resin 环氧树脂coating or rock sample with ~ 环氧树脂涂层或涂有环氧树脂的岩石试件strength of ~ 环氧树脂的强度 equipotential 等位，等电位excavations 峒室，开挖rock movements caused by ~ 开挖引起的岩石位移(移动) extensometers 伸长计，变形测定仪 ~ for boreholes 钻孔伸长计，钻孔变形测定仪 sonor ~ 带声响的变形测定仪 extrados 拱背线，外拱线Ffailure of rock 岩石破坏，岩石断裂 brittle failure, shear failure, tensile 脆性破坏，剪切破坏，拉伸破坏，粘-failure, visco-plastic failure 塑形破坏progressive failure of rock mass 岩体的渐进破坏 failure of dam foundations 坝基破坏failure of rock slopes 岩石边坡破坏,,failure of tunnels and caverns 隧道与峒室破坏 failure criterion 破坏准则，断裂准则 failures 破坏fall of rock 岩石冒落，冒顶 faults in rock 岩石中的断层boling of ~ 岩石断层锚固~ and engineering works 岩石断层与工程施工 filling material in ~ 岩石断层中的冲填材料 slides along ~ 沿岩石断层的滑动 felspar 长石filling material 填充物，填充材料effect of percolating water in ~ 填充物中渗水的影响 tests on ~ 填充物试验 finite element method(f. e. m.)of 岩石应力分析的有限元方法numerical stress analysisfissuration porosity 破坏的多孔性 fissure in rock 岩石中的裂纹，岩石中的裂缝~ along dam heel 沿坝跟(踵)岩石裂缝 classification of ~ 岩石裂缝分类~ and compression strength 岩石裂缝与抗压强度 deformation of ~ 岩石裂缝变形~ and effective elasticity 岩石裂缝与有效弹性 estimates of extent of ~ 岩石破裂的程度估计 grouting of ~ 岩石裂缝注浆~ over pressure tumels 压力隧洞上方的岩石裂缝 rock slide along ~ 沿岩石裂缝的岩石滑动 ~ and stability 岩石裂缝与稳定性~ and stress distribution 岩石裂缝与应力分布 tensile strength and average length of 抗拉强度与岩石裂缝平均长度 ~water flow in ~ 岩石裂缝中的水流Water pressure in ~ 岩石裂缝中的水压力 flood, dam failure caused by 涌水引起的大坝破坏 flow of rock masses 岩体流，泥石流 continuous flow, discontinuous flow 连续流与间断流 flow of water in rock masses 岩石中的水流,,convergent or divergent flow 汇集流与发散流 foliation, plane of 生叶面，叶理面，分层面 foundation 基础fractures of rock 岩石断裂，岩石裂缝correlation between RQD and 岩石质量指标与岩石破裂频率的关系frequency of ~flow of water in ~ 岩石裂缝中的水流plane of ~ 岩石破裂面 friction 摩擦angle of ~ 摩擦角angle of ~ for different rocks 不同岩石的摩擦角 tests for angle of ~ 摩擦角试验coefficient of ~ 摩擦系数coefficient of ~ for filling material 填充材料的摩擦系数 internal ~, internal ~ angle 内摩擦，内摩擦角 friction factor 摩擦系数~ among faults 断层间的摩擦系数~ for rock on rock 岩石对岩石的摩擦系数~ and shear strength 摩擦系数与抗剪强度 friction force 摩擦力Ggabbro 辉长岩galleries 水平隧道，水平坑道，巷道discharge ~ 卸压隧道 pressurized ~ 压力隧道，受压隧道 gap 裂口，间隙，缝隙 gas, underground storage of 地下储油库 gauge 量规，量表，传感器strain ~ 应变传感器rosette of ~ 玫瑰花瓣的应变片丛 geodetic 测地的，大地测量学的，测地学的geological mapping 地质图geo1ogy 地质学，地质概况~ of dam sites 坝址的地质概况~ and rock grouting 地质概况与岩石注浆,,~ and rock mechanics 地质学与岩石力学~ of undersround power station 地下电站地质学，地下发电厂房的地质概况geomorphological 地形的geophone 小型地震仪，地音探测仪 geophysical tahniques 地球物理学方法Georgia Institute of Technology 乔治亚工业学院，乔治亚理工学院geothermal gradient 地热梯度，地温梯度 glacier 冰河，冰川gneiss 片麻岩~ for dam foundations 用于坝基的片麻岩effect of water on ~ 水对片麻岩的影响kaolinized ~ 高岭土化的片麻岩permeability of ~ 片麻岩的渗透性，片麻岩的渗水性 gouge 沟，凿孔，断层泥 granite 花岗岩compression strength of ~ 花岗岩的抗压强度creep curve of ~ 花岗岩的蠕变曲线rebound number of ~ 花岗岩的回弹数strain-stress curve for ~ 花岗岩的应变-应力曲线weathered ~ 风化花岗岩gravity dams 重力坝Griffith,Hoek theory of rupture of 岩石的格里非斯-虎克断裂理论 rocks grout curtains under dams 坝下的注浆帷幕water seepage through ~ 透过坝下注浆帷幕的渗水性 grouting 注浆，灌浆~ with cement 水泥注浆consolidation of rock by ~ 岩石注浆加固~ pressure 注浆压力~ of rock round tunnels 隧道周围的岩石注浆~ with silicates 硅酸盐注浆，注入硅酸盐浆液techniques of ~ 注浆技术~ of tunnels 隧道注浆gunite 压力喷浆，喷射水泥砂浆，砂浆 gypsum 石膏,,Hhalf-space homogeneous elastic 半空间均质弹性的elastic half-space 弹性半空间fissured and continuous ~ 裂隙及连续弹性半空间 loaded halfspace 受灾半空间hardness of rocks 岩石的硬度heat flow, equation for 热流动方程，热传递方程 Heim?s hypothesis 赫米假设Heim?s paradox 赫米自相矛盾论，赫米似是而非论 hexagonal 六边形的，六角形的 homogeneous zones 均质区horizontal stress 水平应力~ in dam foundation 坝基础中的水平应力~ zone from hydrostatic pressure 静水压引起的水平应力区 hydraulic gradient 水力梯度hydraulic potential lines 水力势线hydrodynamic force on rock mass 作用于岩体上的动水压力 hydrogeology 水文地质学hydro power tunnels 水力隧洞hydrostatic pressure 静水压力~ on dam foundation 作用于坝基础上的静水压力distribution of ~ 静水压力分布~ and residual stress in rock 岩石中的静水压力与原岩应力~ on rock mass 作用于岩体上的静水压力 ~ in rock salt 岩质盐矿中的应力 stresses round pressure tunnels 静水压力的压力隧洞周边应力 caused by ~Iice 冰discontinuous flow of ~ 不连续冰流~ in rock fissures 岩石裂隙中的冰 ideal stress 理想应力igneous rocks 火成岩,,immersed and partly immersed rock 侵入及部分侵入岩体 massesimmersion 浸水，浸入 impregnated 渗入的，饱和的 impregnation 注入，浸渗 in situ tests and measurements 现场试验与测量 in situ bore hole tests 现场钻孔试验 in situ compression tests 现场压力试验 in situ permeability tests 现场渗透试验，现场渗水试验 in situ plate bearing tests 现场承载板试验 induration 固结Intitution of Civil Engineering，London 伦敦土木工程研究所，伦敦土木工程学院International Committee on Large 国际大坝委员会 Dams(ICOLD)International Society of rock mechanics 国际岩石力学协会，国际岩石力学学会interstitial water 间隙水intrinsic curve 固有曲线，本质曲线definition of ~ 固有曲线的定义 intrinsic zone 固有区intrados 拱内圈，拱底面 ion 离子isotropic rock mass 各向同性岩石 Istituto Sperimentale Modelli e Structure(ISMES)Jjack 千斤顶cylindrical ~ 液压千斤顶 field tests with ~ 用千斤顶完成的现场试验 ~ in toe of dam 位于坝趾的千斤顶 jacking test 冲击试验，千斤顶加载试验joint 节理~ meter 节理测量仪 ~in rock 岩石中的节理 classification of ~ 节理分类~ and cohesion 节理与粘结力,,~ and critical angle of slopes 节理与边坡临界角 ~and differences between laboratory 节理与变形、弹性的实验室与现场试验and in-situ tests of deformation, of 结果之间的偏差 elasticityorientation of ~ 节理方向 shearing at ~ 节理面剪切 spacing of ~ 节理间距 strength of ~ 节理强度 ~ and strength of rock 节理与岩石强度Jurassic rock 侏罗纪岩石Kkaolinization 高岭土化作用，高岭石化作用 Kelvin,Voight model for rock 开尔文-维埃特岩石变形模型 deformationskinetic energy of rock masses 岩体的动能LLaboratoric Nacional de Engenharia 里斯本…… Civil，LisbonLaboratory tests 试验室试验 ~ on rock material or filling material 岩块或充填材料的实验室试验 ~ on crushing strength 试验室破碎强度试验 ~ on shear strength 试验室剪切强度试验 ~ on water percolation 试验是渗水试验 ~ on wave velocity 波速试验室试验 landslide 山崩，崩塌的泥石 Laplace equation 拉普拉斯方程 Lasalle Research Laboratory，Montreal 蒙特利尔拉斯尔研究实验室 lava 熔岩，火山岩 leakage 漏，渗漏 lias 青石灰岩 limestone 石灰岩compression strength of ~ 石灰岩的抗压强度 ~ for dam foundations 用于坝基建造的石灰岩 elasticity of ~ 石灰岩的弹性 permeability of ~ 石灰岩的渗透性,,strain-stress curves of ~ 石灰岩的应变-应力曲线 swelling of ~ 石灰岩膨胀，石灰岩剪胀 line-load tests 线载荷试验 ~ for antisotropy 各向异性线载荷试验 ~ for tensile strength 抗拉强度线载荷试验 lining 支护，衬砌stresses in ~ 支护体中应力 ~ of tunnel 隧道支护 lip 边，缘lithology 岩石学，岩性学 load cells 压力盒，载荷传感器 load,strain diagram 载荷-应变图 loading 加载，载荷consolidation under ~ 施载加固rate of ~ in test 试验中的加载率 ~ on a slope 边坡上的载荷 loss of water 渗水，漏水~ under dam 坝体渗水~ from tunnels 隧道渗水 Lugeon 罗吉恩~ grouting techniques 罗吉恩注浆技术 ~ unit 罗吉恩系统Mmacrofractures 宏观裂纹~ and permeability 宏观裂纹与渗透性 malm 石灰质砂，泥灰砂 Malm limestone 马尔蒙石灰岩 manifestation 现象，体现，表现形式 manometer (流体)压力表 marble 大理石marl-clay sandstone 灰泥质砂岩 marls 泥灰，泥灰土 permeability of ~ 泥灰土的渗透性 power station in ~ 修建于泥灰土中的发电站,,mechanical properties of rock material 岩石矿物材料的力学性质Mercali scale 麦氏级metamorphic rock 变质岩mica schist 云母片岩 micaceous quartzite 云母石英岩 microfissures 微裂隙~ induced by compression 受压引起的微裂隙~ and permeability 微裂隙与渗透性 microfractures 微观破坏，、微观断裂 mining engineering 采矿工程 mineralogy 矿物学model testing 模型试验~ of dam abutments 坝体支撑的模型试验~ of dam 坝体模型试验 ~ of percolation of water 渗水性模型试验 ~ of reservoir basin 水库体模型试验 ~ of rock mass 岩体模型试验 ~ of sliding surface 滑动面模型试验 ~ of underground power station 地下电站模型试验modulus 系数，模数，模量 dynamic modulus 动态模量 effective modulus 有效模量 ~ in situ testing of rock mass 岩石模量现场试验 ~ laboratory tests模量试验室试验 static ~ 静态模量 ~ in stratified rock mass 层状岩体的模量 moduus of deformation or bulk 边形模量或体积模量 modulus modulus of elasticity(Young modulus) 弹性模量(杨氏模量) modulus of rigidity 刚度模量 Mohr circle 莫尔圆examples of use of ~ 莫尔圆应用实例 mole-for tunnel excavation without 全断面隧道掘进机-用于隧道的非爆破blasting 掘进moment， displacements caused by 力矩引起的位移 momentum equation 力矩方程,,moraine 冰碛，冰碛层 mortar，grouting with 注入砂浆，砂浆注浆mudstone 泥岩mylonite 糜棱岩NNational Coal Board，Britain 英国国家煤炭局(部) needle test, for anisotropy 各向异性针击试验 Newtons law for movement of rock 岩体运动的牛顿定律 massOodometer 里程表，测距仪 oozing 浸出，徐徐流出 openings 峒室，巷道 ~ in rock masses 岩体中巷道circular ~ 圆形巷道，圆形峒室 parallel circular ~ 平行圆形峒室rectangular ~ 方形峒室，矩形巷道 square ~ 四边形巷道 stress and strain about ~, due to 巷道周围的应力应变，原岩应力引起的residual stress; due to hydrostatic 应力应变，巷道中静水压引起的应力应pressure in the tunnel 变ophite 绿辉岩的一种 orthogonal 正交的，直角的 oval-shped 椭圆形的overburden 上覆岩层，抵抗线grout preesure and ~ 注浆压力与上覆岩层minimum ~ for pressure tunnel 压力隧道的最小上覆层厚度 overcoring method for measuring 岩石中原岩应力测量的向下垂直钻孔residual stresses in rock 取芯法overstrained rock，round tunnels 隧道周围的过渡应变岩石Pparallelepipeds 平行六面体 pegmatite 结晶花岗岩 penstock 闸门,,percolation 渗透percolation of water through rock 水渗透岩石 Darcy?s law for ~ 达西岩石渗水定律 Longitudinal ~ 岩石纵向渗水 primary and secondary ~ 主要和次要岩石渗水 radial ~ 径向岩石渗水 test for ~ under dam foundations 坝基础下岩石渗水试验 permeability of rock to air 岩石向大气的渗透性permeability of rock to water 岩石向水的渗透性 compression stress and ~ 抗压强度与岩石的渗水性correlation of ~ with mechanic 岩石渗水性与力学性质、波速的关系properties; with wave velocitygrouting and ~ 注浆与岩石渗透性 Lugeon nut for ~ 罗吉恩的岩石渗水难题 tensile stress and ~ 抗拉强度与岩石渗透性 tests for ~ 岩石渗透性试验permeability factor K 渗透性系数 Permian rocks 二叠纪岩石 perviousness渗透性，渗水性 perviousness of rock 岩石透水性 petroghaphic properitesof rocks 岩石的岩相性质 petrography 岩相学，岩石记述学 photoelastic methods 光弹性方法 phyllite 千枚岩，硬绿泥岩 phyllite quartzite 硬绿岩质石英石 physical properties of rock 岩石的物理性质 piezometers 压力计，压强计 piezometric line 压力线，自由水面线 pilot tunnels 导峒，超前导峒pipes，theory of thick elastic 厚壁弹性管理论，厚壁弹性筒理论 plastic blocks，transmission of stress 应力波穿过塑性区的传播 through plastic deformation of rock 岩石的塑性变形 plasticity of rock 岩石的塑性 plate,bearing tests for deformations 承载板变形试验 theory of ~ 承载板变形试验理论,,point,load test for anisotropy 点载荷各向异性试验 Poiseuille?sformula 泊赛尤尼公式 Poisson?s ratio 泊松比compression stress and ~ 压应力与泊松比 effective value of ~ in rock masses 岩体中泊松比的有效值 pore pressure 孔隙压力 test for ~ 孔隙压力试验 porosity 多孔性，孔隙性 ~ of grout curtain 注浆帷幕的孔隙性 ~ of rock, elasticity, erosion 岩石的孔隙性，弹性，腐蚀 porosity index 孔隙指数porous media,flow of water in 多孔介质中水的流动 porphyry 斑岩Portueuese National Research 葡萄牙国家研究实验室 Laboratorypower stations 地下电站different type of underground power 不同类型的地下电站 stationrock mechanics for underground 地下电站岩石力学 power stationprecast concrete 预制混凝土 pressure，relation of percolation to 渗透性与压力的关系 pressure cell 压力盒，压力传感器 pressure chamber test压力室试验 pressure gradient 压力梯度 pressure pipe 压力管，压力隧洞defective air valve in ~ 压力隧洞的安全气阀 pressure shaft 压力井pressure tunnel 压力隧道，压力隧洞 failures of ~ 压力隧洞的破坏grouting round ~ 压力隧洞周围注浆 minimum overuurden above ~ 压力隧洞的最小厚度上覆层~ adjacent to rock slopes 与岩石边坡临近的压力隧洞最小厚度上覆层,,~ for different types of rocks and 不同类型岩石和巷道的最小厚度上覆galleries; in rock liable to plastic 层;易于塑性变形岩石中的压力隧洞的deformation; under alluvium; 最小厚度上覆层;冲积层下压力隧洞的under horizontal rock surface 最小厚度上覆层;水平岩层表面下压力隧洞的最小厚度上覆层 seepage from ~ 压力隧洞的渗漏 stresses in ~ 压力隧洞岩石中的应力 stresses in ~ from hydrostatic 静水压力引起的压力隧洞岩石中的应pressure 力theory of ~ 压力隧洞理论 precipitation 沉淀，沉淀物 prestressed concrete 预应力混凝土 propane 丙烷pseudo,shear 准剪切pulvino (pressure distribution slab) 压力分布板 punching shear test 冲剪试验Qquality index 质量指标，质量指数 rock quality designation 岩石质量指标radial percolation index 径向渗透系数 quartz 石英permeability of ~ 石英的渗透性 quartz,diorite 石英-闪长岩 quartz-mica gneiss 石英-云母片麻岩 quartz-mica schist 石英-云母片岩 quartz-monzonite 石英-二长岩 quartzite 石英岩，硅岩 creep of ~ 石英岩的蠕变 ~ for dam foundations 用作坝基的石英岩 fissured ~ 裂隙石英岩 micaceous ~ 云母状石英岩 powdery ~ 粉状石英岩 strain-stress curves for ~ 石英岩的应变-应力曲线 quartzose phyllite 含石英的千牧岩 quartzose shale 含石英的页岩,,Rradial percolation test 径向渗透试验 ramp 斜面rate of loadng 加载率rayoliterebound number 回弹数rectangle 矩形，长方形 strains round a ~ 矩形洞室岩石中的应变strains under a loaded ~ 受载矩形洞室的应变 reinforced concrete 钢筋混凝土 relaxation of rock masses 岩体的松弛 Repeatable Acoustic Seismic Source 可重复的声学地震源 reservoir 水库，蓄水池displacement of embankments of ~ 水库坝堤的位移 variation of water level in ~ 水库水面(位)的变化 residual stresses in rock 岩石中的残余应力，岩石原岩应力 ~ and elasticity 岩石原岩应力与弹性 measurements of ~ 岩石原岩应力测量 relaxation from ~ 原岩应力释放，原岩应力松弛static equilibrium method 静力平衡法 resins, impregnation of rock with 岩石中注入彩色树脂 colouredresistance quotient 阻力商，阻力系数~ of jointed rock 节理岩石的阻力系数 resistivity 阻力，抵抗力resonance waves 共振波reversible deformations 可逆变形，弹性变形 rheology 流变学，流变能力rigidity，modulus of 刚度模量rock arch 岩石拱rock bolt extensometer 岩石锚杆伸长仪，岩石锚杆变形测量仪rock bolting 岩石锚杆，岩石锚杆支护 rock bolts，different types of 不同类型的岩石锚杆 rock burst 岩爆rock fill dam 岩石土坝，岩石充填坝,,rock load 岩石载荷~ on lining 作用于支护体上的岩石载荷 ~ on steel supports 作用于刚支架上的岩石载荷 rock mass 岩体classification of ~ 岩体分类structure and anisotropy of ~ 岩体结构与各向异性 rock material 岩石，岩石矿物材料 rock quality designation(RQD) 岩石质量指标 rock slide 岩石滑坡rosette 应变片rupture of rocks 岩石破坏Griffith,Hoek theory of ~ 岩石破坏的格里菲斯-虎克理论point of ~ 岩石破坏点 Torre?s theory of ~ 托里岩石破坏理论Ssafety factor 安全系数~ against sliding 滑坡安全系数~ for dam 大坝安全系数 ~ for tunnel 隧道安全系数 salt mine 盐矿creep in ~ 盐矿蠕变sandstone 砂岩compressibility of ~ 砂岩的可压缩性 permeability of ~ 砂岩的渗透性stresses in ~ 砂岩种的应力 swelling of ~ 砂岩的膨胀，砂岩的剪胀saturation swelling stress 饱和膨胀压力 scale effect 尺寸效应~ in compression tests 压缩试验中的尺寸效应~ in deformation and displacement 变形和位移试验中的尺寸效应 tests ~ in elasticity tests 弹性试验中的尺寸效应 schist 片岩schistosity 片理，片岩性 plane of ~ 片理面,,scour 清理，净化sedimentary rock 沉积岩slopes in ~ 沉积岩边坡seepage 渗流，渗出~ from pressure tunnel 从隧道中渗出~ in rock mass 岩体中的渗流 ~ under dam 坝下渗流seismic wave tests on rock; on dam site 岩石的，坝址的地震波试验seismic wave tests for detecting 检测初始滑动，软弱岩石的地震波试验incpient slides; weakening rockseismic wave tests inside gallery 峒室内的地震波试验 sesmic wave velocity 地震波速度。
从测不准原理看软件测试的不充分性
《自动化技术与应用》２００８年第２７卷第８期仪器仪表与检测技术Instrumentation and Measurment从测不准原理看软件测试的不充分性吉向东（襄樊学院物理系，湖北 襄樊 ４４１０５３）摘 要：从测不准原理的哥本哈根解释出发，讨论了导致软件测试不充分性的根本原因。
通过对软件测试过程各阶段的逐一分析，将软件测试视为一种特殊的测量过程，应用测不准原理的哥本哈根解释，给出了导致软件测试不充分性的根本原因。
由于单元测试和集成测试中编写的测试代码对原有代码的干扰，以及在整个测试过程中发现缺陷后对系统所做的更改，使软件测试的对象随着测试过程的进行不断的发生变化，软件测试的系统是一个随着软件测试过程的进行而不断改变的系统，根据测不准原理，如果测试系统对被测系统的影响不可以忽略，待测系统是不可能得到充分测试的。
关键词：测不准原理；软件测试；不充分性中图分类号：ＴＰ３１１．５ 文献标识码：Ａ 文章编号：１００３－７２４１（２００８）０８－００１８－０３Discussions on Insufficiency of Software T estingAccording to the Uncertainty PrincipleJI Xiang-dong(Department of Physics, Xiangfan University, Xiangfan 441053, China)Abstract: Insufficiency of software testing is discussed from the view of the Copenhagen School on the Heisenberg uncertaintyprinciple. The fundamental cause of insufficiency of software testing is analysed at each phase of software testing. The original code is disturbed from the testing code for unit testing and integrity testing. So according to uncertainty principle, sufficiency testing to software system is impossible if the effect from test system can not be ignored.Keywords: uncertainty principle; software testing; insufficiency收稿日期：２００８－０３－１８１ 引言虽然不同研究人员给出了不同的判断软件测试充分性的准则［１－４］。
复杂受限系统的鲁棒性分析与控制
客观评价： 澳大利亚皇家墨尔本理工大学 Xinghuo Yu 教授（IEEE Fellow, IEEE 工业电子协会主席） 在论文(IEEE Transactions on Systems, Man, and Cybernetic: Systems, vol. 47, pp. 783 – 793, 2017)中评价： “A novel Lyapunov functional is proposed for sampled control in [35], which greatly reduces the conservatism of the existing results” 。文献[35]为代表性论 文[1]。 西安交通大学徐宗本教授（中国科学院院士）在论文(IEEE Transactions on Cybernetics, vol. 46, pp. 1189-1201, 2016)中指出： “Markov chain has achieved great success in many machine learning tasks such as speech recognition [18], biogeography-based optimization [19], DNA sequence analysis, neural networks synchronization [20] „„” 。文献[20]为 代表性论文[2]。 澳大利亚西悉尼大学 Wei Xing Zheng 教授（IEEE Fellow）在论文(IEEE Transactions on Neural Networks and Learning Systems, vol. 26, pp. 2346-2356, 2015) 中评价 : “ More recently, a study on filtering with partial information on mode jumps has been carried out for a class of Markov jump systems in [18]. A nonsynchronous filter is designed with nonstationary modes transition that is capable of capturing the different degree of nonsynchronous jumps between system modes and filters. It has been verified that the designed filter is effective, outperforming the mode-independent filter in achieving a better filtering performance index in the energy-to-peak sense” 。文献[18]为代表性 论文[5]。 东北大学张化光教授（IEEE Fellow）在论文(IEEE Transactions on Neural Networks and Learning Systems, vol. 28, pp. 740-752, 2017) 中 评 价 : “ the less conservatism synchronization criteria for neural networks have been obtained in [30] ” 。文献[30] 为代表性论文[7]。 意大利米兰理工大学 Hamid Reza KarimiI 教授 （科睿唯安 “全球高被引科学家” ） 在论文(IEEE Access, vol. 5, 2017) 中 评 价 : “ a novel TDLF was proposed in [21] to reduce conservativeness and enlarge the allowable sampling” 。文献[21]为代表性论文[1]。
酰胺的英文结构
酰胺的英文结构Amides: The Versatile Molecular StructuresAmides are a class of organic compounds that have captured the attention of chemists and researchers worldwide due to their diverse applications and intriguing structural properties. These compounds, characterized by the presence of a carbonyl group (C=O) and a nitrogen atom (N), have become an integral part of numerous fields, ranging from pharmaceuticals and materials science to agricultural and industrial processes.At the heart of amides lies a unique molecular arrangement, where the carbonyl carbon is covalently bonded to a nitrogen atom, forming a planar structure. This arrangement, known as the amide bond, is a crucial feature that contributes to the versatility and stability of amide molecules. The resonance stabilization of the amide bond, resulting from the delocalization of electrons, endows amides with remarkable chemical and thermal stability, making them resistant to hydrolysis and other common chemical reactions.One of the most fascinating aspects of amides is their ability to participate in a wide range of chemical transformations. Amides canundergo various reactions, such as hydrolysis, reduction, and substitution, allowing for the synthesis of a diverse array of compounds. This versatility has made amides indispensable in the field of organic synthesis, where they serve as important precursors and intermediates in the preparation of a myriad of complex molecules.In the realm of pharmaceuticals, amides have emerged as a prominent structural motif in the development of numerous therapeutic agents. The amide bond's stability and ability to form hydrogen bonds with biological targets have rendered amides as highly effective pharmacophores. Many clinically approved drugs, including analgesics, anti-inflammatory agents, and antidepressants, incorporate amide functionalities within their molecular structures.Beyond their pharmaceutical applications, amides have also found widespread use in the field of materials science. The unique properties of amides, such as their ability to form hydrogen-bonded networks and their thermal stability, have made them valuable components in the development of advanced materials. Amides are commonly employed in the synthesis of polymers, where they contribute to the mechanical and thermal properties of the resulting materials. Additionally, amides have found applications in the design of supramolecular assemblies, liquid crystals, and self-healing materials.In the agricultural sector, amides have become indispensable as key components in various agrochemicals. Amide-based pesticides, herbicides, and fungicides have been developed to effectively control pests, weeds, and plant diseases, contributing to the enhancement of crop yields and the overall sustainability of agricultural practices.The versatility of amides is further exemplified in their industrial applications. Amides are utilized in the production of lubricants, surfactants, and coatings, where their unique properties, such as their ability to form hydrogen bonds and their thermal stability, make them valuable additives. Additionally, amides are employed in the synthesis of various polymers, including polyamides (nylons), which have found widespread use in the textile and engineering industries.In the realm of analytical chemistry, amides have found their way as important structural moieties in the development of analytical techniques and tools. The amide bond's stability and the ability to participate in various intermolecular interactions have made amides valuable in the design of chromatographic stationary phases, biosensors, and diagnostic assays.The ubiquity of amides in diverse fields underscores the profound impact of these remarkable molecular structures on our daily lives.From the development of life-saving pharmaceuticals to the creation of advanced materials and the enhancement of agricultural practices, amides have firmly established themselves as indispensable components in the ever-evolving landscape of scientific and technological advancements.As the scientific community continues to explore the depths of amide chemistry, the future holds immense promise for the discovery of new and innovative applications of these versatile molecular structures. The ongoing research in this field promises to unlock novel avenues for the betterment of human welfare, environmental sustainability, and the advancement of scientific knowledge.。
Stability robustness of networked control systems with respect to packet loss
Automatica43(2007)1243–1248/locate/automaticaBrief paperStability robustness of networked control systemswith respect to packet lossଁShawn Hu,Wei-Yong Yan∗Department of Electrical and Computer Engineering,Curtin University of Technology,GPO Box U1987,Perth6845,AustraliaReceived16March2005;received in revised form14August2006;accepted18December2006AbstractThis paper is concerned with stability analysis of discrete-time networked control systems over a communication channel subject to packet loss whose behavior is modeled by an i.i.d Bernoulli process with a packet dropping probability bounded by a constant.A necessary and sufficient condition for stability is obtained.A packet dropping margin is introduced as a measure of stability robustness of a system against packet dropping,and a formula for it is derived.A design method is proposed for achieving a large margin subject to a constraint that the system has a set of prescribed nominal closed-loop poles.᭧2007Elsevier Ltd.All rights reserved.Keywords:Networked control systems;Packets;Stability robustness;Probability;Pole placement1.IntroductionNetworked control systems(NCSs)are systems with a feedback loop closed via a real-time shared media network. The study of such systems has received increasing attention in recent years because of ubiquity of the Internet(Chow& Tipsuwan,2001).The advantages of NCSs over conventional or hardwired control include reduction of system wiring and ease of installation.On the other hand,such factors as bandwidth constraints,packet delays,and packet dropping often affect the performance of an NCS or even cause instability.There has been some work on the effects of these factors.For example, in Tatikonda and Mitter(2004),Tatikonda,Sahai,and Mitter (2004),Liu,Elia,and Tatikonda(2004),control problems were formulated and studied for an NCS subject to bandwidth con-straints.A stability analysis of NCSs with time delay was pre-sented in Zhang,Branicky,and Phillips(2001)and a method to obtain a maximum allowable delay bound was provided in ଁThis paper was not presented at any IFAC meeting.This paper was recommended for publication in revised form by Associate Editor Ioannis Paschalidis under the direction of Editor Ian Petersen.∗Corresponding author.Tel.:+61892667931;fax:+61892662584.E-mail addresses:xiaolin.hu@.au(S.Hu),w.yan@.au(W.-Y.Yan).0005-1098/$-see front matter᭧2007Elsevier Ltd.All rights reserved. doi:10.1016/j.automatica.2006.12.020Kim,Lee,Kwon,and Park(2003).LQG controller design prob-lems of NCSs with delay were studied in Nilsson,Bernhardsson, and Wittenmark(1998),and Hu and Zhu(2003).Stability of NCSs with a communication network subject to packet dropping has received much attention as well.In the continuous-time case,an NCS was modeled as an asynchronous dynamical system with rate constraints on events(Zhang et al., 2001),where the network was treated as a switch that closes at a certain rate corresponding to a packet dropping probability (PDP).It was shown there that a sufficiently fast sampling rate can guarantee stability of the system.In Montestruque and Antsaklis(2003,2004),the authors considered stability of a model-based NCS i.e.an NCS with an additional model used for estimating the plant state between transmission times and generating a control signal.A stability condition was obtained for the Try-Once-Discard network protocol in Walsh,Ye,and Bushnell(1999).In the discrete-time case,the packet dropping process of a communication network is usually modeled as either an i.i.d Bernoulli process or a Markov chain,which is more general. With such a characterization of the packet dropping process, an NCS can be viewed as a special jump system.The mean-square stability of jump systems has been well studied,see e.g.Ji,Chizeck,Feng,and Loparo(1991),Feng,Loparo,Ji,1244S.Hu,W.-Y.Yan/Automatica43(2007)1243–1248and Chizeck(1992),Costa and Fragoso(1993),Ghaouli and Aitrami(1996),and Fang and Loparo(2002).As a conse-quence,stability results in Ji et al.(1991)and Costa and Fragoso (1993)naturally lead to a necessary and sufficient condition for stability of an NCS.Expressed in terms of a set of linear matrix inequalities,this condition has been used to check the stability of an NCS when the controller is constructed using the LQG method(Azimi-Sadjadi,2003).It has also been used for designing an H∞controller in Seiler and Sengupta(2005).An Markov chain for describing the packet dropping process has been considered for other purposes in e.g.Ling and Lemmon (2003b),Zhang,Ding,Frank,and Sader(2004),and Gupta, Spanos,Hassibi,and Murray(2005).More specifically,a for-mula for the power spectral density was presented in Ling and Lemmon(2003b),the problem of designing an observer-based residual generator was discussed in Zhang et al.(2004),and the problem of designing a decoder and an encoder for optimal LQG control was considered in Gupta et al.(2005).When the packet dropping process is modeled by an i.i.d process with a given PDP,a necessary and sufficient condition for mean-square stability of NCSs can be found in Ling and Lemmon (2003a).In the one-dimensional case,a stabilization scheme was provided in Hadjicostis and Touri(2002).In this paper,by modeling the packet dropping of a com-munication network as an i.i.d Bernoulli process,we carry on stability analysis of a discrete-time NCS with static state feed-back where the PDP of the communication network is bounded by a known upper bound.It can easily be argued that it makes more sense to assume the availability of an upper bound of the PDP than the exact value of the PDP,which is assumed to be known in the literature such as Azimi-Sadjadi(2003)and Ling and Lemmon(2003a).Another aim of the paper is to address stability robustness of the system with respect to packet drop-ping by introducing a quantity termed a packet dropping mar-gin(PDM),which is defined to be the maximum PDP that an NCS can tolerate before becoming unstable.A formula for the margin is derived in the paper as well.Finally,we discuss how a controller can be designed to achieve a large margin subject to the constraint that the resulting NCS has certain guaranteed transient performance.A design method based on a robust pole placement technique is proposed.The paper is organized as follows.In Section2,an NCS is described.Section3presents a stability analysis of the NCS. Section4deals with the problem of designing a state feedback law to achieve a suboptimal PDM subject to performance spec-ifications on nominal closed-loop poles.Conclusions are given in Section5.2.System descriptionA typical NCS as depicted in Fig.1consists of three com-ponents:a nominal plant to be controlled,a network such as the Internet,and a controller.In this paper,it is assumed that the nominal plant is described byx k+1=Ax k+B1u k+B2w k,(2.1)Fig.1.A networked control system.where x k∈R n is the state,u k∈R m is the control input,w k∈R r is an external input,and A,B1,B2are constant matrices with appropriate dimensions.We assume that the full state of the plant is transmitted to the controller in the form of packets through the network.The network is assumed to be modeled byˆx k= k x k,(2.2) where k is an i.i.d Bernoulli random process.At any time in-stant k, k has two possible values0and1.The value0indicates that the state vector x k is completely lost during transmission while the value1indicates that x k is successfully transmitted. The probability that k=0,commonly termed a PDP,is invari-ant with time k and measures how reliable a network is.Though it is a standard assumption in the literature that the PDP of an NCS is known,this assumption may be too strong due to the following observations:1.The complexity of the network environment often makes itdifficult to determine the exact PDP associated with an NCS.2.For an NCS with n 2,even if it is stable for a given PDP,the system may become unstable when the PDP reduces due to the network improvement,which will be shown by an example in Section3.As such,in this paper we assume the availability of an upper bound on the PDP instead of the exact PDP.Moreover,it is clear that any packet dropping occurring at the plant input can be treated as the packet dropping occurring at the plant output as far as the closed-loop system is canceled. Therefore,it suffices to consider the case where packet dropping happens only at the plant output.Unlike a conventional controller,a controller in an NCS re-ceives plant information as input from a network which may be shared by any other type of devices.In this paper,the controller in Fig.1is assumed to be of the state feedback formu k=Kˆx k,(2.3) whereˆx k is the received state vector at time instant k and K∈R m×n is a feedback gain.Because of the assumption on the network,it is seen that the received state vectorˆx k is either equal to the transmitted state vector x k or zero.It is convenient to refer to the combination of the nominal plant and the network in Fig.1as a networked plant,and the eigenvalues of A+B1K in(2.1)–(2.3)as the nominal closed-loop poles of the NCS.In the literature,the stability of an NCS is commonly defined as follows,see e.g.Feng et al.(1992),S.Hu,W.-Y.Yan/Automatica43(2007)1243–12481245Ghaouli and Aitrami(1996),Ling and Lemmon(2003a),and Montestruque and Antsaklis(2003).Definition1.The networked plant(2.1)–(2.2)is said to be ms-stabilized(stabilized in the mean-square sense)by the controller (2.3)if there holds lim k→∞E{ x k 2}=0for any initial state x0∈R n and w k=0.The NCS(2.1)–(2.3)is said to be nominallystable if it is ms-stable for the PDP equal to0.3.Stability analysisThe main purpose of this section is to derive a necessary and sufficient condition for an NCS to be stable in the case where only an upper bound of the PDP is known.The condition will lead to the introduction of a new concept of PDM,which can be used to quantitatively measure the degree of stability robustness of the system with respect to packet dropping.First we need the following lemma which gives two equiva-lent necessary and sufficient conditions for stability of an NCS in the case of a known PDP.Thefirst condition was given with-out proof in Ling and Lemmon(2003a)and the second condi-tion has not been obtained before.Lemma2.The networked plant(2.1)–(2.2)with the PDP equal to a constant is ms-stabilized by(2.3)if and only if either of the following two conditions holds:(i)[ A⊗A+(1− )A K⊗A K]<1,(3.1) where⊗denotes a Kronecker product and (·)is the spec-tral radius of a matrix,andA K=A+B1K.(3.2) (ii)For any given symmetric positive definite matrix Q,there isa unique symmetric positive definite solution to the equationP= A T P A+(1− )A T K P A K+Q.(3.3)Proof.Due to the paper length limitation,we only prove the condition in(i)as the other condition in(ii)can be derived fromfirst principles.First note that when w k=0,the state covariance k+1can be expressed ask+1=E[x k+1x T k+1]=A E[x k x T k]A T+A E[x k x T k]E[ k]K T B T1+B1K E[ k]E[x k x T k]A T+B1K E[ 2k]E[x k x T k]K T B T1(3.4)i.e.k+1= A k A T+(1− )(A+BK1) k(A+BK1)T(3.5)due toE[ k]=E[ 2k]=1− .With the identitycs(MY N)=(N T⊗M)cs(Y)one obtainscs( k)=H k cs( 0),(3.6) whereH= A⊗A+(1− )A K⊗A Kand cs(·)is the column vector formed by the columns of a matrix.Thus,it follows from(3.1)that cs( k)converges to zero as k tends to infinity.By definition,the system(2.1)–(2.3) is stable.To prove the necessity of(3.1),let us assume that the system (2.1)–(2.3)is stable.Then it is easy to show that the state covariance matrix will converge to zero for any complex initial state,which implieslimk→∞H k cs( 0)=0(3.7)for any semi-positive Hermitian matrix 0.Since a Hermitian matrix can be expressed as the difference between two semi-positive Hermitian matrices,Eq.(3.7)holds for any Hermitian matrix 0as well.Furthermore,the equation remains true even for any complex matrix 0due to the decomposition0= 1−j 2,where both 1and 2are Hermitian.Therefore,it follows that H k converges to zero,which is equivalent to (H)<1.Remark3.Based on the above lemma,the following obser-vations can be made:•The NCS is nominally stable if and only if the nominal closed-loop poles of the NCS are strictly inside the unit circle.•B2has no effect on the stability of the NCS(2.1)–(2.3).•In the one-dimensional case,the stability condition(3.1)can be simplified as| (A2−A2K)+A2K|<1.(3.8)It should be pointed out that the stability of the system for a given PDP does not necessarily imply the stability for any smaller PDP,which may result when the network becomes more reliable.This can be seen by considering the NCS withA=0.5−10−1,B1=1002,K=−0.21−10.9.This system is ms-stable both for the PDP equal to0and for the PDP equal to0.8,but it is unstable when the PDP equals0.4. As such,it is important to address the following two questions. Under what condition is the system ms-stable for any PDP less than a given bound?What is the largest PDP bound?To answer these questions,let us introduce what will be called the PDM, which can serve as a measure of stability robustness of an NCS with respect to packet dropping.1246S.Hu,W.-Y.Yan /Automatica 43(2007)1243–1248Definition 4.The PDM of the NCS (2.1)–(2.3)is the largest positive bound such that the system is ms-stable for any PDP less than .Obviously,the NCS has to be nominally stable for the PDM to exist.In the one-dimensional case,the following formula for the PDM can be easily derived from (3.8):PDM =⎧⎨⎩1−A 2K A 2−A 2K when |A |>|A K |,∞when |A | |A K |.(3.9)To obtain a formula for the PDM in the general case,the fol-lowing lemma is needed.Lemma 5.Given two constant matrices M 1,M 2∈R n ×n with(M 1)<1,there holdssup { >0; (M 1+ M 2)<1,∀ ∈(0, )}=1 (U),(3.10)where (·)is the largest positive eigenvalue of a matrix andU =(M 1⊗M 2+M 2⊗M 1)(I −M 1⊗M 1)−1M 2⊗M 2(I −M 1⊗M 1)−10.(3.11)Proof.See the Appendix.Theorem 6.If the NCS (2.1)–(2.3)is nominally stable ,its PDMis given by PDM =1,(3.12)whereV =(S ⊗ˆS +ˆS ⊗S)(I −S ⊗S)−1ˆS ⊗ˆS (I −S ⊗S)−10,S =A K ⊗A K ,ˆS=A ⊗A −A K ⊗A K .(3.13)Proof.Notice that A ⊗A +(1− )A K ⊗A K =S + ˆS.Moreover, (S)<1if and only if (A K )<1.Thus,the theorem follows from Lemma 5.Remark 7.It is clear that the NCS (2.1)–(2.3)is ms-stable for any PDP less than if and only if PDM.4.Constrained optimization of PDMA distinct feature of an NCS is that the state information is transmitted across a network.When there is no packet loss during the transmission,the NCS is simply a conventional con-trol system whose behavior is largely determined by the nom-inal closed-loop poles.Therefore,it makes sense to specify or prescribe the performance of an NCS in terms of its nominal closed-loop poles.On the other hand,it is worth noting that the state feedback law which achieves desired closed-loop poles is not unique.The PDM introduced in Section 3measures the maximum amount of packet loss that an NCS can tolerate before becoming unstable.The larger the margin,the less sensitive the NCS to packet loss.While the PDM is readily computable via the formula (3.12)for a given controller,its dependence on the controller is so complicated that it is hard to directly maximize the PDM through the design of a controller by using (3.12).In this section,we seek a state feedback law which not only places the nominal closed-loop poles at given locations but also optimizes the PDM in a certain sense.Specifically,we consider the following problem:Problem 1.For the NCS (2.1)–(2.3),find a state feedback gain K ∈R m ×n which maximizes the PDM and places the nominal closed-loop poles at given locations.To solve this problem,we need the following lemma which reveals the relationship between the PDM and a condition num-ber associated with the feedback gain.Lemma 8.If the NCS (2.1)–(2.3)is nominally stable ,there holdsPDM 1− 2(A K )22(A K ) A 22− 2(A K ),(4.1)where A K =A +B 1K , · 2and 2(·)denote the spectral normand the spectral condition number of a matrix ,respectively .Proof.The lemma obviously holds if 22(A K ) A 22−2(A K )<0.It suffices to prove the lemma in the case where22(A K ) A 22− 2(A K )>0.To this end,we show that for anygiven PDP ,the networked plant (2.1)–(2.2)is ms-stabilized by (2.3)if there holds<1− 2(A K )22(A K ) A 22− 2(A K ).(4.2)Let A ⊗A be a perturbation onto (1− )A K ⊗A K .ByBauer–Fike theorem,for any given ˆ∈spec [(1− )A K ⊗A K + A ⊗A ],there exists a ∈spec (A K ⊗A K )such that |(1− ) −ˆ| 2(A K ⊗A K ) A ⊗A 2,(4.3)where spec (·)is the spectrum of a matrix.It is easy to showthat 2(A K ⊗A K )= 22(A K )and A ⊗A 2= A 22.Then,weobtain|ˆ |−(1− )| | 22(A K ) A 22(4.4)implying that|ˆ | [ 22(A K ) A 22−| |]+| |.(4.5)From (4.2)and 2(A K ) | |,we have[ 22(A K ) A 22−| |]+| |<1.(4.6)With (4.5),we have |ˆ|<1.As ˆ is arbitrary,the networked plant (2.1)–(2.2)is ms-stabilized by (2.3).S.Hu,W.-Y.Yan /Automatica 43(2007)1243–12481247Table 1The packet dropping margin and p p 12345PDM0.100.2740.3370.3350.335It can be seen that the lower bound of the PDM in (4.1)is positive when the nominal plant (2.1)is unstable.In addition,this bound only depends on the condition number of A K if the nominal closed-loop poles,i.e.the eigenvalues of A K ,are prescribed in advance.More precisely,the bound is inversely proportional to the condition number 2(A K ).This latter ob-servation suggests that a state feedback law which achieves a large PDM while placing the nominal closed-loop poles at de-sired locations can be found by solving the problem of mini-mizing 2(A K )subject to the constraint spec (A K )= ,where is a given set of self-conjugate complex numbers of cardi-nality n .Such a problem can be solved by using an ODE-based algorithm in Lam and Yan (1997)as it is essentially a robust pole placement problem,which has been well discussed in the literature.The following example shows that the proposed algorithm is effective.Example 4.1.Consider the networked plant (2.1)–(2.2)withA =⎡⎢⎣1.70.41.8−2−0.8−3.1−3.2−1.5−1.2⎤⎥⎦,B 1=⎡⎢⎣0.5000.510.5⎤⎥⎦and the desired nominal closed-loop poles −0.2±0.2j and −0.6.We invoke the algorithm in Lam and Yan (1997)with G 0=[111111]as the starting point,where the corresponding K 0yields a PDM of 0.108.The algorithm results in a final feedbackgain K ∗=[−2.1475.071−0.5762.221−3.0816.287]which yields a PDM of 0.335.Table 1shows the variation of the PDM associated with G p for p =1,2,3,4,5.5.ConclusionsIn this paper,we discussed the stability of an NCS subjectto packet loss during the transmission of plant information to the controller over a network.A necessary and sufficient condi-tion for stability was derived in the case where an upper bound of the PDP is given.In addition,the PDM was introduced to measure the degree of stability robustness of an NCS with re-spect to packet dropping.A formula for computing the PDM was obtained.An optimization method was proposed for de-signing a state feedback law to achieve a large PDM subject to the constraint that the NCS has prescribed nominal closed-loop poles.It goes without saying that all the obtained results can easily be extended to the case where the transmission of a control signal is also subject to packet dropping.AcknowledgmentsThis work has been partially supported by an ARC research grant.The constructive comments and suggestions from the anonymous reviewers and the Associate Editor are very much appreciated.Appendix A.Proof of Lemma 5First,we define∗ sup { >0; (M 1+ M 2)<1,∀ ∈(0, )}, ∗ min { >0; (M 1+ M 2)=1}.(A.1)Due to continuity and (M 1+ ∗M 2)=1,we have ∗ ∗.From the definition of ∗,it is clear that ∗ ∗.Thus,we obtain ∗= ∗.Since M 1+ M 2is a real matrix and any eigenvalue of (M 1+ M 2)⊗(M 1+ M 2)is the product of two eigenvalues of M 1+ M 2,it can be seen that∗=min { >0;det [I −(M 1+ M 2)⊗(M 1+ M 2)]=0},(A.2)where det (·)is the determinant of a matrix.Notice that I −(M 1+ M 2)⊗(M 1+ M 2)= 2( 2 1+ 2+ 3),(A.3)where =1/ ,1=I −M 1⊗M 1,2=−M 2⊗M 1−M 1⊗M 2,3=−M 2⊗M 2.Let = 2 1+ 2+ 3.Since 2=0,we obtain ∗=1max { >0;∃w =0s .t . w =0}.(A.4)Let be a fixed positive number for which there exists w =0such that w =0.Then,we have [− −1100][0w ]=0.With theidentity − −1100 = I 0 1I0I I 2− −1100− 3 × I 10I = I 0 1I ( U 1−U 2)× I 10I ,(A.5)where U 1=[0I I 2]and U 2=[ −1100− 3],it is easy to see thatthe equation w =0is equivalent to ( U 1−U 2)v =0i.e.U −11U 2v = v where v =[ 1w w ].Therefore, satisfies w =0for some w =0if and only if is an eigenvalue of the matrix U −11U 2.From (A.4),it follows that ∗=1/ (U −11U 2)=1/ (U).ReferencesAzimi-Sadjadi, B.(2003).Stability of networked control systems in the presence of packet losses.Proceedings of the 42nd IEEE conference on decision and control (pp.676–681).1248S.Hu,W.-Y.Yan/Automatica43(2007)1243–1248Chow,M.Y.,&Tipsuwan,Y.,(2001).Network-based control systems:A tutorial.In Proceedings of IECON’01,the27th annual conference of the IEEE 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Tatikonda,S.,Sahai,A.,&Mitter,S.(2004).Stochastic linear control overa communication channel.IEEE Transactions on Automatic Control,49,1549–1560.Walsh,G.C.,Ye,H.,&Bushnell,L.,(1999).Stability analysis of networked control systems.In Proceedings of the American Control Conference’99.(V ol.4,pp.2876–2880).Zhang,P.,Ding,S.X.,Frank,P.M.,&Sader,M.,(2004).Fault detection of networked control systems with missing measurements.In Proceedings of thefifth Asian Control Conference.(V ol.2,pp.1258–1263).Zhang,W.,Branicky,M.S.,&Phillips,S.M.(2001).Stability of networked control systems.IEEE Control Systems Magazine,21,84–89.Shawn Hu received his B.Eng.degree in Ma-terial Science from Beijing Polytechnic Univer-sity,M.EngSc.in Telecommunications and Net-working from Curtin University of Technology.Now he is a Ph.D.student in the Departmentof Electrical and Computer Engineering,CurtinUniversity of Technology.His research interestsinclude stability theory,stability robustness andoptimization in networked controlsystems.Wei-Yong Yan received the B.S.degree inMathematics from Nankai University,Tianjin,in1983,the M.S.degree in Systems Sciencefrom Academia Sinica.Beijing.in1986,andthe Ph.D.degree in Systems Engineering fromthe Australian National University,Canberra,in1990.From1990to1992,he worked as a ResearchFellow in the Department of Systems Engi-neering,the Australian National University.Hewas a Lecturer in Applied Mathematics at theUniversity of Western Australia from1993to 1994prior to joining the Nanyang Technological University in Singapore first as a Lee Kuan Yew Fellow and later as a Senior Lecturer in the School of Electrical and Electronic Engineering.Since1998,he has been a Senior Lecturer in the Department of Electrical and Computer Engineering at Curtin University of Technology,Perth,Australia.His current research interests are in the areas of control and signal processing.。
随机马尔可夫跳变系统的弹性动态输出反馈控制
随机马尔可夫跳变系统的弹性动态输出反馈控制作者：李艳恺陈谋吴庆宪来源：《南京信息工程大学学报（自然科学版）》2018年第06期摘要本文討论了随机噪声影响下马尔可夫跳变系统的弹性动态输出反馈控制问题.在系统随机干扰和控制输入扰动的情况下，设计的弹性控制器可以确保闭环系统的依概率渐近稳定性.通过运用随机微分方程理论和线性矩阵不等式技术对系统进行稳定性分析，获得了系统依概率渐近稳定的充分条件和控制器增益.最后通过数值算例和直升机系统仿真验证了所提弹性动态输出反馈控制方法的有效性.关键词随机马尔可夫跳变系统;弹性控制;动态输出反馈控制;依概率渐近稳定;线性矩阵不等式中图分类号 TP273文献标志码 A0 引言马尔可夫跳变系统是一类特殊的随机切换系统，它的切换规律依赖于转移概率矩阵.随着对马尔可夫跳变系统的深入研究，很多实际系统控制的问题，例如电子通信、生物医学以及经济分析等，都可以利用马尔可夫跳变系统的控制方法来处理[1-3] .近年来，很多控制领域知名专家在马尔可夫跳变控制系统问题上取得了很多研究成果[4-8] .另一方面，由于随机噪声的存在，实际系统的控制性能往往会受到影响，甚至导致系统的不稳定.随着随机控制系统理论的不断发展，很多关于随机噪声的抑制问题得到解决[9-10] .如文献[11]讨论了关于随机拉格朗日系统的输出反馈控制问题;文献[12]研究了非线性随机系统的状态反馈H ∞控制问题;文献[13]给出了随机非线性系统的稳定性法则.对于马尔可夫跳变系统，随机噪声也是普遍存在的.通常情况下，随机噪声存在于各个独立的子系统中，并且与模态间的随机跳变相互独立.随机噪声的存在使得马尔可夫跳变系统问题变得更加复杂.文献[14]分别采用状态反馈反步控制方法和输出反馈反步控制方法处理了一类随机马尔可夫跳变系统的控制问题;文献[15]解决了奇异随机马尔可夫跳变系统的稳定性问题.这些研究工作很大程度上促进了随机马尔可夫跳变系统的理论发展，也为许多实际工程上的控制问题提供了可行的解决方案.由于在很多实际工程应用中，系统状态往往很难测量，或者测量的成本极高，因此，输出反馈控制方案成为处理这类问题的首选方案.在文献[8，16]中，应用动态输出反馈控制器处理连续时间马尔可夫跳变系统和连续时间奇异马尔可夫跳变系统问题，并取得了良好的控制效果.然而，由于控制器设备的老化、计算器维数限制以及传感器灵敏性过强或过弱等，都会使系统的控制过程中混入一定的扰动.因此，在设计控制器的时候充分考虑到这些扰动对系统的影响是有必要的.针对这一问题，一些学者设计了弹性控制器，提高了闭环系统的鲁棒性.文献[17]研究了带有脉冲异步切换系统的弹性控制器设计问题;文献[18]结合基于干扰观测器控制方法，设计抗干扰弹性控制器，讨论了多干扰下的马尔可夫跳变系统的稳定性问题.本文主要研究了随机马尔可夫跳变系统的弹性动态输出反馈控制器设计问题.首先，在系统混有随机干扰、控制器存在扰动的情况下设计动态输出反馈控制器，保证闭环系统稳定.然后，利用随机控制理论、李雅普诺夫稳定性理论以及线性矩阵不等式技术，分析闭环系统的稳定性，获得可解的充分条件.最后通过数值仿真和直升机控制系统算例验证本文所提控制方案的有效性.4 总结本文研究了随机噪声和输入扰动下随机马尔可夫跳变系统的弹性动态输出控制问题.为了保证闭环系统的依概率渐近稳定性，设计了弹性动态输出反馈控制器，并应用随机控制系统理论、李雅普诺夫稳定性理论以及线性矩阵不等式技术，获取了保证系统具有相应控制性能的可解的充分条件.最后通过一个数值算例和无人直升机系统模型验证了本文所提方法的可行性.参考文献References[ 1 ]Boukas E K.Stochastic switching systems：analysis and design[M].Berlin，Germany：Birkhauser，2005[ 2 ] Mao X，Yuan C.Stochastic differential equations with Markovian switching[M].London：Imperial College Press，2006[ 3 ] ksendal B.Stochastic differential equations-an introduction with applications[M].New York：Springer-Verlag，2003[ 4 ] Li Y，Sun H，Zong G，et al，Composite anti-disturbance resilient control for Markovian jump nonlinear systems with partly unknown transition probabilities and multipledisturbances[J].International Journal of Robust and Nonlinear Control.2017，27（14）：2323-2337[ 5 ] Fei Z，Gao H，Shi P.New results on stabilization of Markovian jump system with time delay[J].Automatica，2009，45（10）：2300-2306[ 6 ] He S，Liu F.Robust peak-to-peak filtering for Markov jump systems[J].Signal Processing，2010，90（2）：513-522[ 7 ] Zhang L，Boukas E K.Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities[J].Automatica，2009，45（2）：463-468[ 8 ] Farias D P，Geromel J C，Val J B R，et al.Output feedback control of Markov jump linear systems in continuous-time[J].IEEE Transactions on Automatic Control，2000，45（5）：944-949[ 9 ] 吳昭景.随机引论[M].北京：科学出版社，2016WU Zhaojing.Stochastic introducing[M].Beijing：Science Press，2016[10] Jazwinski A H.Stochastic processes and filtering theory[M].New York：Academic Press，1970[11] Cui M，Wu Z，Xie X.Output feedback tracking control of stochastic Lagrangian systems and its application[J].Automatica，2014，50（5）：1424-1433[12] Zhang W，Chen B S.State feedback H ∞ control for a class of nonlinear stochastic systems[J].Siam Journal on Control & Optimization，2006，44（6）：1973-1991[13] Zhang W.Stability criteria of random nonlinear systems and their applications[J].IEEE Transactions on Automatic Control，2015，60（4）：1038-1049[14] Wu Z，Xie X，Shi P，et al.Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching[J].Automatica，2009，45（4）：997-1004[15] Zhao Y，Zhang W.New results on stability of singular stochastic Markov jump systems with state-dependent noise[J].International Journal of Robust and Nonlinear Control，2016，26（10）：2169-2186[16] Kwon N K，Park I S，Park P G，et al.Dynamic output-feedback control for singular Markovian jump system：LMI Approach[J].IEEE Transactions on Automatic Control，2017，62（10）：5396-5400[17] Zong G，Wang Q.Robust resilient control for impulsive switched systems under asynchronous switching[J].International Journal of Computer Mathematics，2015，92（6）：1143-1159[18] Li Y，Sun H，Zong G，et al.Anti-disturbance control for time-varying delay Markovian jump nonlinear systems with multiple disturbances[J].International Journal of Systems Science，2017，48（15）：3186-3200[19] Chen M，Chen W.Disturbance-observer-based robust control for time delay uncertain systems[J].International Journal of Control，Automation and Systems，2010，8（2）：445-453[20] Raptis I A，Valavanis K P，Vachtsevanos G J.Linear tracking control for small-scale unmanned helicopters[J].IEEE Transactions on Control Systems Technology，2012，20（4）：995-1010Resilient dynamic output feedback control forstochastic Markovian jump systemLI Yankai 1 CHEN Mou 1 WU Qingxian 1[ 7 ] Zhang L，Boukas E K.Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities[J].Automatica，2009，45（2）：463-468[ 8 ] Farias D P，Geromel J C，Val J B R，et al.Output feedback control of Markov jump linear systems in continuous-time[J].IEEE Transactions on Automatic Control，2000，45（5）：944-949[ 9 ] 吴昭景.随机引论[M].北京：科学出版社，2016WU Zhaojing.Stochastic introducing[M].Beijing：Science Press，2016[10] Jazwinski A H.Stochastic processes and filtering theory[M].New York：Academic Press，1970[11] Cui M，Wu Z，Xie X.Output feedback tracking control of stochastic Lagrangian systems and its application[J].Automatica，2014，50（5）：1424-1433[12] Zhang W，Chen B S.State feedback H ∞ control for a class of nonlinear stochastic systems[J].Siam Journal on Control & Optimization，2006，44（6）：1973-1991[13] Zhang W.Stability criteria of random nonlinear systems and their applications[J].IEEE Transactions on Automatic Control，2015，60（4）：1038-1049[14] Wu Z，Xie X，Shi P，et al.Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching[J].Automatica，2009，45（4）：997-1004[15] Zhao Y，Zhang W.New results on stability of singular stochastic Markov jump systems with state-dependent noise[J].International Journal of Robust and Nonlinear Control，2016，26（10）：2169-2186[16] Kwon N K，Park I S，Park P G，et al.Dynamic output-feedback control for singular Markovian jump system：LMI Approach[J].IEEE Transactions on Automatic Control，2017，62（10）：5396-5400[17] Zong G，Wang Q.Robust resilient control for impulsive switched systems under asynchronous switching[J].International Journal of Computer Mathematics，2015，92（6）：1143-1159[18] Li Y，Sun H，Zong G，et al.Anti-disturbance control for time-varying delay Markovian jump nonlinear systems with multiple disturbances[J].International Journal of Systems Science，2017，48（15）：3186-3200[19] Chen M，Chen W.Disturbance-observer-based robust control for time delay uncertain systems[J].International Journal of Control，Automation and Systems，2010，8（2）：445-453[20] Raptis I A，Valavanis K P，Vachtsevanos G J.Linear tracking control for small-scale unmanned helicopters[J].IEEE Transactions on Control Systems Technology，2012，20（4）：995-1010Resilient dynamic output feedback control forstochastic Markovian jump systemLI Yankai 1 CHEN Mou 1 WU Qingxian 1。
要稳也要快的作文
要稳也要快的作文Finding a balance between stability and speed in our daily lives is a common struggle for many people. 在我们日常生活中找到稳定和速度之间的平衡是许多人共同的挑战。
On one hand, stability is essential for maintaining a sense of security and well-being. 一方面，稳定是保持安全感和幸福感的重要因素。
Without stability, there is a lack of predictability and control in our lives, which can lead to increased stress and anxiety. 没有稳定性，我们的生活就会缺乏可预测性和控制性，这会导致增加的压力和焦虑。
Stability provides a foundation for us to build upon, allowing us to focus on our goals and aspirations with confidence. 稳定性为我们提供了一个建立基础，让我们可以有信心专注于自己的目标和愿望。
However, solely prioritizing stability can sometimes hinder progress and growth, as it may prevent us from taking risks or stepping out of our comfort zones. 然而，单纯地优先考虑稳定有时也会阻碍进步和成长，因为它可能会阻止我们冒险或走出舒适区。
Speed, on the other hand, is often associated with progress and efficiency. 另一方面，速度通常与进步和效率联系在一起。
水沟模板加固方法
水沟模板加固方法Water ditch reinforcement is a critical task to ensure the stability and safety of the surrounding areas. There are several methods that can be used to strengthen water ditch templates, and each method has its own advantages and disadvantages.水沟模板加固是确保周围地区稳定和安全的重要任务。
有几种方法可以用来加固水沟模板，每种方法都有其自身的优缺点。
One method to reinforce water ditch templates is by using geotextiles. Geotextiles are permeable fabrics that can be placed in between the soil and the water ditch templates to help with erosion control and soil stabilization. This method is relatively cost-effective and easy to install, making it a popular choice for reinforcing water ditch templates.加固水沟模板的一种方法是使用土工布。
土工布是一种透水的织物，可以放置在土壤和水沟模板之间，以帮助控制侵蚀和土壤稳定。
这种方法成本相对较低，安装也比较简单，因此成为加固水沟模板的常用选择。
Another method to strengthen water ditch templates is by using concrete. Concrete can be poured into the water ditch templates to create a solid and durable barrier. This method is highly effective in providing stability and preventing erosion, but it may be more costly and time-consuming compared to other methods.加固水沟模板的另一种方法是使用混凝土。
描写泥石流的英文作文
描写泥石流的英文作文Title: The Terrifying Fury of Mudslides。
Introduction:Nature's wrath can be awe-inspiring and terrifying, none more so than the phenomenon known as mudslides or mudflows. These powerful torrents of mud, rocks, and debris have the capacity to wreak havoc on landscapes and communities, leaving devastation in their wake. In this essay, we will delve into the characteristics, causes, and consequences of mudslides, shedding light on their destructive force.Characteristics of Mudslides:Mudslides, also referred to as debris flows, are rapid mass movements of saturated debris down a slope. Unlike landslides, which primarily involve rock and soil, mudslides contain a significant proportion of water, givingthem a fluid-like consistency. This high water content enables mudslides to travel at astonishing speeds, often exceeding 35 miles per hour (56 kilometers per hour).Causes of Mudslides:Several factors can contribute to the initiation of mudslides, with rainfall and steep terrain being primary catalysts. Intense or prolonged rainfall saturates the soil, reducing its stability and increasing the likelihood of slope failure. In regions with steep topography, gravity exacerbates the downward flow of water-saturated debris, initiating mudslides. Human activities such as deforestation, construction, and improper land use can also amplify the risk of mudslides by destabilizing slopes and altering natural drainage patterns.Consequences of Mudslides:The consequences of mudslides can be catastrophic, inflicting significant loss of life, property damage, and environmental degradation. As mudslides descend slopes,they engulf everything in their path, including homes, roads, and vegetation. Communities situated in vulnerable areas are particularly at risk, facing displacement, injury, and trauma in the aftermath of a mudslide event. Furthermore, the deposition of sediment and debris canalter river courses, disrupt ecosystems, and compromise water quality, exacerbating the long-term impacts of mudslides.Case Study: The Oso Mudslide。
稳定的 翻译
稳定的翻译Stability is an essential aspect of various aspects of our lives. Whether it is in our personal relationships, our careers, or our financial situations, stability plays a crucial role in providing us with a sense of security and peace of mind. This article will explore the concept of stability and its significance in our lives.Stability can be defined as a state of balance or equilibrium. It refers to a situation where things are predictable, consistent, and reliable. In personal relationships, stability is essential for fostering trust and emotional well-being. When we have a stable relationship with our loved ones, we feel secure and confident in our connection with them. This stability allows us to open up, share our thoughts and feelings, and strengthen the bond we have with them. On the other hand, instability in relationships can lead to uncertainty, anxiety, and conflict, making it difficult to maintain a healthy and happy connection.Similarly, stability in our careers is crucial for professional growth and satisfaction. When we have a stable job, we can rely on a regular income, which enables us to meet our financial obligations and plan for the future. Stable employment also provides us with a sense of purpose and accomplishment, as we can develop our skills, build expertise, and progress in our chosen field. On the contrary, job instability can cause stress, job dissatisfaction, and financial hardship. It can make it challenging to meet our basic needs and affect our mental and emotional well-being.Financial stability is another critical aspect of our lives. It refers to the ability to manage our finances effectively and be prepared forunexpected expenses. When we are financially stable, we have a steady income, manage our expenses wisely, and have savings to fall back on during difficult times. Financial stability allows us to have a sense of control over our lives, reduce stress related to money, and achieve our long-term financial goals. Conversely, financial instability can lead to debt, financial stress, and limited opportunities for personal and professional growth. It can also affect our overall well-being, relationships, and mental health.Furthermore, stability is vital in societal and political contexts. A stable society is one where there is social order, peace, and harmony. It is characterized by institutions that function effectively, laws that are enforced fairly, and a sense of justice and equality for all. Stability in society promotes economic development, social cohesion, and overall well-being. On the other hand, social instability can lead to conflicts, social unrest, and economic decline. Political stability is also crucial for a nation's progress and prosperity. It allows for effective governance, policy implementation, and a conducive environment for economic growth and development.In conclusion, stability plays a significant role in various aspects of our lives. Whether it is in our personal relationships, careers, finances, or society as a whole, stability provides us with a sense of security and peace of mind. It allows us to develop meaningful connections, pursue our goals, and lead fulfilling lives. Therefore, it is essential to cultivate and maintain stability in all areas of our lives to ensure our overall well-being and happiness.。
Geotechnical Engineering and Soil Mechanics
Geotechnical Engineering and SoilMechanicsGeotechnical engineering, a specialized branch of civil engineering, plays a critical role in ensuring the stability and safety of structures built upon the earth. It delves into the intricate world of soil mechanics, exploring the behavior of soils under various conditions to inform design and construction practices. Understanding the complexities of soil, a heterogeneous and unpredictable material, is fundamental to creating sound infrastructure. Soil, a product of weathered rock and organic matter, presents a fascinating tapestry of different types, each with unique characteristics. From coarse-grained gravel and sand to fine-grained silt and clay, the properties of soil dictate its strength, permeability, and compressibility. Geotechnical engineers employ a variety of laboratory and field tests to analyze these properties, providing crucial data for their calculations and predictions. The significance of geotechnical engineering becomes particularly evident in the design of foundations. As the literal bedrock of any structure, foundations must be meticulously engineered to distribute loads effectively and prevent settlement or failure. Factors such as soil type, groundwater conditions, and the magnitude of structural loads are carefully considered in determining the appropriate foundation type, whether it be shallow footings, deep foundations, or specialized solutions like rafts or piles. Slope stability is another crucial area where geotechnical principles are applied. Natural and man-made slopes, often susceptible to landslides, necessitate careful analysis to ensure their stability. Engineers assess factors like slope geometry, soil strength, and the presence of water to determine potential failure planes and implement stabilization measures like retaining walls, soil nailing, or vegetation reinforcement. Furthermore, the construction of underground structures like tunnels and pipelines demands a thorough understanding of soil behavior. Excavations can significantly alter stress distributions within the soil, potentially leading to ground movements and structural distress. Geotechnical engineers meticulously analyze soil properties and groundwater conditions to predict potential risks and design appropriate support systems to maintainstability throughout the construction process. In conclusion, geotechnical engineering, intricately linked to the principles of soil mechanics, is an indispensable field in civil engineering. Its application extends far beyond the construction of buildings and bridges, encompassing a wide range of infrastructure projects. Through a combination of scientific knowledge, meticulous analysis, and innovative solutions, geotechnical engineers ensure the stability and safety of our built environment, safeguarding against potential hazards and promoting sustainable development.。
稳定用英语怎么说
稳定用英语怎么说导读：我根据大家的需要整理了一份关于《稳定用英语怎么说》的内容，具体内容：稳定有稳固安定;没有变动的意思。
如水位、情绪、局势等;在各学科领域都可以用来形容某种体系或状态等，如稳定乳状液、稳定流动等。
在心理学上稳定指的是一种状态，指所处的环境或者心境在一定量的时...稳定有稳固安定;没有变动的意思。
如水位、情绪、局势等;在各学科领域都可以用来形容某种体系或状态等，如稳定乳状液、稳定流动等。
在心理学上稳定指的是一种状态，指所处的环境或者心境在一定量的时间之内不会轻易变化。
那么你知道吗?下面来学习一下吧。
稳定英语说法1：stable稳定英语说法2：steady稳定英语说法3：level off稳定相关英语表达：稳定度 Stability ; degree of stability ; Stableness ; degree of fixation经济稳定 economic stability ; stabilizacja ekonomiczna ; economic stabilization ; economic steadiness社会稳定 social stability ; social stabilization ; societal stability ; stabilization of society电压稳定 voltage stability ; voltage stabilization ; voltage stable ; valtage stability稳定网络 stabilization network ; stabilizing network ; Stable Network稳定基金 EFSF ; stabilization fund ; SFRF ; European Financial Stability Facility保持稳定 Stable ; maintaining stability ; hold steady ; remain stable稳定时间 Settling time ; Stability time ; stabilization time ; steady time稳定平台 stabilized platform ; stable platform ; stabilizer stable platform ; stable flat稳定的英语例句：1. The price of oil should remain stable for the rest of 1992.油价会在1992年剩下的时间里保持稳定。
离散广义系统的有限时间控制
离散广义系统的有限时间控制∗龚文振【摘要】本文利用Lyapunov 方法研究了线性离散广义系统的有限时间控制问题。
针对该系统的开环情形，给出了其有限时间稳定的充分条件。
在此基础上，设计状态反馈控制器，给出了其闭环系统是有限时间有界的充分条件。
特别地，针对具有外源干扰线性离散广义系统，我们也给出了控制器设计方法和保证其闭环系统有限时间有界的充分条件。
最后通过数值算例验证了该方法的有效性。
%In this paper, the finite-time control problem is considered for discrete linear sin-gular systems by virtue of Lyapunov’s method. The sufficient conditions for the finite-time stability of the open-loop discrete linear singular systems are given. Based on the conditions, a state controller is designed and thesufficient conditions for the finite-time boundedness of the closed-loop system composed by the state controller and the discrete linear singular system are presented. In particular, we consider a discrete linear singular system subject to an ex-ogenous output, and provide a designing method of controller and the sufficient conditions for the finite-time boundedness of the closed-loop system composed by the controller and discrete linear singular system subject to an exogenous output. Finally, a numerical example illustrates the validity of the proposed approach.【期刊名称】《工程数学学报》【年(卷),期】2013(000)002【总页数】14页(P217-230)【关键词】离散广义系统;外部扰动;有限时间有界【作者】龚文振【作者单位】玉林师范学院数学与计算机科学系，玉林 537000【正文语种】中文【中图分类】TP131 引言在实际的控制系统中，有时有限时间稳定要比经典Lyapunov稳定更为有趣，主要原因在于：经典的Lyapunov稳定性描述的是系统在无穷时间区间上的动态行为，不能反映系统在具体时间间隔中的动态行为，而有限时间稳定主要是考虑一定的时间内，系统的状态能保持稳定就可以了，这有助于复杂的系统的设计要求，也就是条件放得更宽了．所谓的有限时间稳定就是指当系统的初值偏离平衡点一定范围时，在给定的有限时间区间内，系统的状态仍然在我们预先给定的范围内．在有限时间稳定的研究中，1961年Dorat首先提出了系统的有限时间控制问题[1]．在实际应用中，一个系统在运行时经常会受到外部干扰，在理想状态下运行的可行性很小，为了解决系统在受外部扰动下的有限时间控制问题，意大利学者Amato提出了“有限时间稳定(Finite-Time Stability)”和“有限时间有界(Finite-Time Boundedness)”的概念[2]，从而使得控制系统具有更好的鲁棒性能和抗扰动性能．关于有限时间控制问题的研究，已取得了一些成果，如意大利学者Amato等就非线性二次经典系统给出了保证其有时间稳定和有限时间有界的充分条件[3-5]；Zhu等人研究了具有外源干扰的不确定离散系统的有限时间控制问题[6]；冯俊娥等就参数不确定性和外部扰动的线性广义系统的有限时间控制问题给出了部分结果[7]；孙甲冰等通过引入状态-控制对的满秩变化，将广义系统转化成线性系统，再利用经典线性系统的有限时间控制相关结果，来解决奇异系统的有限时间控制问题[8]；Zhang等研究了广义系统的随机保性控制问题[9]．这些结果基本是关于经典控制系统和广义时间连续控制系统的研究，关于离散广义系统的有限时间控制问题的结果尚为少见．本文主要研究离散广义系统的有限时间控制问题，将有限时间稳定的概念推广到离散广义系统，通过等价分解，把离散广义系统分解为与之等价的微分代数系统，利用线性矩阵不等式(LMI)分析其有限时间稳定性，给出状态反馈控制，实现闭环系统的有限时间稳定和具有外部扰动的离散广义系统的有限时间有界的充分条件．2 问题描述与定义考虑如下的离散广义系统其中k∈N为时间变量；E，A∈Rn×n，B∈Rn×m，G∈Rn×q皆为定常矩阵，rank(E)=r<n，x(k)∈Rn，u(k)∈Rm，w(k)∈Rq分别为状态向量，控制向量和外源干扰向量．我们的目的是找到适当的状态反馈控制器使得(1)和(2)构成的闭还系统轨线在指定的有限时间内具有预期的界限．如果(E，A)是正则的和因果的，则存在两个可逆矩阵P，Q，使得其中Ir，A11∈ Rr×r，Ir为单位阵，A12∈ Rr×(n−r)，A21∈ R(n−r)×r，而A22 ∈ R(n−r)×(n−r)可逆．令则系统(1)等价于如下的离散广义系统首先给出离散广义系统有限时间有界稳定的概念．引入如下记号：这里conv{x(1)，x(2)，···，x(l)}表示由n维列向量x(1)，x(2)，···，x(l)所张成的最大的凸面体．由线性代数的知识知，一定存在着h个n维列向量λ1，λ2，···，λh，使得h为适当的正整数[3]．c0，c1为正常数，ε0为非负常数．作为例子，设其中则可取定义1 给定大于1的正整数N，离散广义系统关于(Γ0，Γ1，N)是有限时间稳定的(FTS)，如果(5)的解x(k)满足当x(0)∈ Γ0时，都有x(k)∈ Γ1，k=1，2，···，N．定义2 给定大于1的正整数N，称离散广义系统关于(Γ0，Γ1，Γ2，N)是有限时间有界的(FTB)，如果(6)的解x(k)满足当x(0) ∈Γ0∧w(0)∈ Γ2时，都有x(k)∈ Γ1，k=1，2，···，N．引理1[10] 对于给定的对称阵如下条件是等价的：引理2[8] 对于给定的对称阵当S1可逆时，如下两个条件是等价的：或当S3可逆时，如下两个条件是等价的：3 主要结果对于系统(1)的无受迫、无干扰系统(5)，如果(E，A)是正则的和因果的，作适当的变换易知其等价于定理1 系统(7)关于(Γ0，Γ1，N)是有限时间稳定的，如果存在对称正定矩阵P1∈Rr×r和常数及γ≥1，0<δ<1，满足下面的条件：其中证明对任意的由条件(d)易知，．考虑系统(7)的Lyapunov函数k ∈ {0，1，···，N}，对于系统(7)的解我们有由条件(e)易知V(x1(k))≤γV(x1(k))．令则必有>N，否则，若≤N，我们有这与的定义矛盾，所以>N．因此，对任意的有由条件(c)易得，由条件(b)及引理2，我们有另一方面，所以从而下面我们回来考虑如下的离散广义控制系统((E，A)不一定具有因果性)：类似于上面的讨论，存在可逆阵P，Q，使得式(3)成立．令易知(8)等价于如下系统为了设计的需要，我们假设rank(A22，B2)=n−r．从而可以找到适当的矩阵H21，H22，H22可逆，使得如下的矩阵是可逆的，记进而有(A22B2)H−1=(In−r0)，记代入(9)可得其中定理2 若存在矩阵L1，对称正定阵X1，及常数γ≥1，0≤δ<1，满足下面的条件：其中则系统(10)在控制(此时的作用下，闭环系统关于(Γ0，Γ1，N)是有限时间稳定的．证明在控制(此时的作用下，系统(10)的闭环系统为令对(e)的两边分别乘以易得也就是考虑闭环系统(11)的Lyapunov函数对于系统(11)的解类似于定理1的证明，我们有V(x1(k))≤γV(x1(k))．同理，令下面我们证明事实上，由条件(c)易得，由条件(b)及引理2，我们有另一方面所以从而下面考虑具有外源干扰的情形如果(E，A)是正则的和因果的，作适当的变换易知其等价于其中定理3 系统(13)关于(Γ0，Γ1，N)是有限时间有界的，如果存在对称正定矩阵P1∈Rr×r和常数γ ≥ 1，0≤ δ<1，0≤ ηs≤1，s=1，2，···，g，满足下面的条件：其中证明对任意的由条件(d)易知，考虑系统(13)的Lyapunov函数(k)+ γw(k)P1w(k)，k ∈ {0，1，···，N}，对于系统(13)的解我们有由条件(e)易知V(x1(k)，w(k))≤γV(x1(k−1)，w(k−1))．令则必有否则，若¯k≤N，我们有从而有这与的定义矛盾，所以>N．因此，对任意的有由条件(c)易得{0，1，2，···，N}．由条件(b)及引理2，我们有另一方面所以从而4 数值算例例1 考虑如下离散广义系统其中令取经计算，可得令γ=1.05，δ=0.5．根据定理2，容易验证在控制u(k)= −x1(k)−x2(k)的作用下，(14)的闭环系统关于(Γ0，Γ1，N)是有限时间稳定的．5 结束语本文研究了一类具有外部扰动的线性离散广义系统的有限时间控制问题，给出了离散广义系统有限时间有界的概念．利用线性矩阵不等式(LMI)方法给出了，无受逼和无干扰的离散广义系统有限时间稳定的充分析条件，进而给出了具有外部扰动的线性离散广义系统的有限时间有界的充分条件，给出了状态反馈控制器的设计方法，实现闭环系统的有限时间稳定．最后通过数值算例验证了该方法的有效性．参考文献：[1]Dorato P.Short-time Stability in Linear Time-varying Systems[M].New York:Polytechic Institnte of Brookly，1961[2]Amato F，Ariola M，Dorato P.Finite-time control of linear systemssubject to parametric uncertainties and disturbances[J].Automatica，2001，37(9):1459-1463[3]Amato F.Sufficient conditions for f i nite-time stability and stabilizationof nonlinear quadratic systems[J].IEEE Transactions on Automatic Control，2010，55(2):430-434[4]Amato F，Ariola M.Finite-time control of discrete-time linearsystem[J].IEEE Transactions on Automatic Control，2005，50(5):724-729 [5]Feng J E，Wu Z，Sun J B.Finite-time control of linear singular systems with parametric uncertainties and disturbances[J].Acta Automatica Sinica，2005，31(4):634-637[6]Zhu L，Shen Y J，Li C C.Finite-time control of discrete-time systemswith time-varying exogenous disturbance[J].Communications in Nonlinear Science and Numerical Simulation，2009，14(2):361-370[7]Amato F，Ariola M，Cosentino C.Finite-time stabilization via dynamic output feedback[J].Automatica，2006，42(2):337-342[8]孙甲冰，程兆林.一类不确定线性奇异系统的有限时间控制问题[J].山东大学学报，2004，39(2):1-6 Sun J B，Cheng Z L.Finite-time control for a kind of uncertain linear singular[J].Journal of Shandong University，2004，39(2):1-6[9]Zhang Y Q，Liu C X，Mu X W.Stochastic f i nite-time guaranteed cost control of Markovian jumping singular systems[J].Mathematical Problemsin Engineering，2011，1(1):1-20[10]Boyd S，Ghaogui L E，Feron E，et al.Linear Matrix Inequalities inSystem and Control Theory[M].Philadelphia:SIAM，1994。
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Chapter8Open ProblemsIn this chapter,we would like to give a list of open and unanswered problems in Mathematical Control Theory.The solutions of these open problems will be very important for the development of modern nonlinear control theory.Expectedly novel mathematical analysis and synthesis tools need to be developed to address these challenging problems.The interested reader should also consult the book[3]for other significant and important open problems in Mathematical Control Theory.Open Problem#1Under what conditions WIOS implies IOS?A qualitative characterization of the IOS property for abstract control systems as discussed in this book has not been available yet.For systems described by ODEs, many qualitative characterizations of the ISS and IOS properties are provided in [21–23].Moreover,Theorem4.1in Chap.4gives a complete qualitative character-ization of the WIOS property:“0-GAOS”+“RFC”+“the continuity with respect to initial conditions and external inputs”implies WIOSA similar qualitative characterization for the IOS property in a general context of abstract dynamical systems as discussed in this book will be very important for control designs and applications.Open Problem#2Development of small-gain techniques for dynamical systems described by Partial Differential Equations(PDEs).Small-gain results have been well studied forfinite-dimensional nonlinear sys-tems described by ordinary differential,or difference,equations(see,e.g.,[8–10] and references therein).However,as of today,there is little research devoted to the development of small-gain techniques for nonlinear systems described by Partial Differential Equations(PDEs).We believe that the small-gain results provided in the present book(Theorems5.1and5.2in Chap.5)will pave the road for the appli-cation of small-gain results to systems described by PDEs.I.Karafyllis,Z.-P.Jiang,Stability and Stabilization of Nonlinear Systems,381 Communications and Control Engineering,DOI10.1007/978-0-85729-513-2_8,©Springer-Verlag London Limited2011Open Problem#3Formulas for the Coron–Rosier methodology.Theorem6.1in Chap.6is an existence-type result.Although its proof is con-structive,it cannot be easily applied for feedback design purposes.The creation of formulas for the Coron–Rosier approach will be very significant for control pur-poses,since the Coron–Rosier approach can allow nonconvex control sets and does not require additional properties for the Control Lyapunov Function.The signifi-cance of the solution of this open problem is also noted in[5].Open Problem#4When is a nonlinear,time-varying,time-delay system stabiliz-able?We have recently provided a positive answer to the above question when the sys-tem only involves state-delay[13].A complete answer to the question of when the nonlinear time-varying system with both state and input delays is stabilizable re-mains open and requires deeper investigation.Nonetheless,it should be mentioned that sufficient,but not necessary,conditions for the solution of the stabilization prob-lem with input delays are proposed in the recent work of Krsti´c[14–16](also see [11]).To our knowledge,a necessary and sufficient condition for stabilizability is missing even for linear time-varying systems with input delays.Open Problem#5Application of small-gain results for distributed feedback design of large-scale nonlinear systems.Large-scale systems are abundant in variousfields of science and engineering and have gained increasing attention due to emerging engineering and biomedical applications.Examples of these applications are from smart grids with green and re-newable energy sources,modern transportation networks,and biological networks. There has been some success with the use of decentralized control strategy for both linear and nonlinear large-scale systems;see[7,19]and many references therein. Clearly more remains to be accomplished in this excitingfield.We feel that small-gain is a very appropriate tool for addressing some of these modern-day challenges. The small-gain results of the present book(Theorems5.1and5.2in Chap.5)make a preliminary step forward toward studying some complex large-scale systems be-yond the past literature of decentralized systems and control.Open Problem#6Extension of the discretization approach for autonomous sys-tems.The discretization approach for Lyapunov functionals was described in Chap.2 (Propositions2.4and2.5).However,as remarked in Chap.2,the discretization ap-proach requires good knowledge of some approximation of the solution map,and its use has been restricted to time-varying systems with special structure(see[1,17, 18]).An extension of the discretization approach for autonomous systems wouldbe an important contribution in stability theory because such a result would al-low the use of positive definite functions with non sign-definite derivative.The re-quired extension of the discretization approach must utilize appropriate differential inequalities in the same spirit as the classical Lyapunov’s approach(without requir-ing knowledge of the solution map or a system with special structure).The recent work in[12]is an attempt in this research direction(see also references therein). However,the problem is still completely“untouched.”Open Problem#7Application of feedback design methodologies to other mathe-matical problems.In this book,we have seen the applications of certain tools of modern nonlinear control theory to problems arising from mathematics and economics.Particularly, we have seen•applications of small-gain results to game theory(see Sect.5.5in Chap.5),•applications to numerical analysis(see Sect.7.3).We believe that feedback design methodologies can be applied with success to other areas of mathematical sciences.Fixed Point Theory(see[6])and Optimization Theory can be benefited by the application of certain tools of modern nonlinear con-trol theory.Corollary5.4in Chap.5already shows that small-gain results can have serious consequences in Fixed Point Theory.Further connections between Fixed Point Theory and Stability Theory are provided by the work of Burton(see[4]and references therein)but are in the opposite direction from what we propose,that is, the work of Burton applies results from Fixed Point Theory to Stability Theory.The efforts for the solution of problems in Game Theory,Numerical Analysis, Fixed Point Theory,and Optimization Theory will necessarily demand the creation of novel results in stability theory and feedback stabilization theory.Therefore,the application of modern nonlinear control theory to other areas of applied mathe-matics will result to a“knowledge feedback mechanism”between Mathematical Control Theory and other areas in mathematics!Open Problem#8Integral input-to-state stability(for short,iISS)in complex dy-namical systems.The external stability results of this book are exclusively targeted at extensions of Sontag’s ISS property and its variants to a very general context of complex dynamic systems.That is,we want to address a wide class of dynamical systems which may not satisfy the semigroup property,motivated by important examples of hybrid sys-tems,switched systems,and time-delay systems.It remains an 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