论文摘要模板

摘要

建立非线性动力系统的模糊模型进而基于该模糊模型对非线性动力系统实施有效的控制是目前非线性系统控制研究的研究方向之一。本论文主要内容涉及复杂非线性动力系统的模糊建模和模糊控制的研究。其中包括：（1）关于超混沌系统的模糊建模及其同步的研究；（2）关于T-S模糊系统的无源性和无源化的研究；（3）关于连续T-S模糊大系统的稳定性分析和鲁棒控制的研究；（4）关于时延T-S 模糊大系统的稳定性分析与系统镇定的研究。

本文的主要创新之处可概括如下：

1. 关于超混沌系统的模糊建模及其同步的研究。

复杂的超混沌系统能产生多于一个正的李雅谱诺夫指数的复杂混沌吸引子。研究超混沌系统间的超混沌同步对保密通信有重要的意义。我们研究了两类典型的超混沌系统的Takagi-Sugeno（T-S）模糊建模。基于模糊模型，设计了相应的模糊控制器去实现超混沌系统间的同步。

2．关于T-S模糊系统的无源性和无源化的研究。

起源于电路理论的系统无源性理论自上世纪70年代以来受到控制领域里学者的关注。关于非线性系统的无源性的研究存在着大量的研究结果，但模糊系统的无源性未得到充分的研究。T-S模糊模型通过模糊集和模糊推理能够有效的表达非线性动力系统。因此，T-S模糊系统的无源性研究有助于非线性控制系统的研究。我们分别研究了带参数不确定的连续和离散T-S模糊系统的无源性的判定准则和状态反馈无源化的设计方法。

3．关于连续T-S模糊大系统的稳定性分析和鲁棒控制的研究。

当今现实物理、工程以及社会系统给系统理论带来的一个巨大挑战是必须面对和克服高维数、非线性的复杂数学模型。在过去的几年中，针对非线性大系统的控制研究受到了相当的关注。非线性大系统的稳定性分析及控制器设计较为困难。一个新的途径是建立非线性大系统的T-S模糊大系统模型，进而基于该模糊大系统模型进行稳定性分析和控制器设计。本文采用分段二次Lyapunov函数来研究模糊大系统的稳定性，取得了保守性更小的稳定性判定准则。并基于该分段二次

模糊控制器的设计方法。使得在该模糊控制器的Lyapunov函数，导出了相应的H

控制下非线性大系统在保证稳定性的同时，系统对外部扰动的抑制达到要求的性

I

能。

4. 关于时延T-S模糊大系统的稳定性分析与系统镇定的研究。

由于实际系统的内部变量信号传递往往存在延迟。本文对子系统内部及子系统间同时存在时延的模糊大系统进行了稳定性分析的研究。基于时延模糊大系统模型，利用Lyapunov-Krasovskii泛函和线性矩阵不等式进行了稳定性分析。得出了由线性矩阵不等式表达的稳定性判定准则。并且研究了如何设计模糊状态反馈控制器去镇定时延模糊大系统。

关键词：非线性动力系统T-S模糊系统超混沌同步时延稳定性H

控制

线性矩阵不等式(LMI)

II

Abstract

The fuzzy modeling and control of nonlinear systems is an important research area in nonlinear control. In this dissertation, we perform the fuzzy modeling and control on complex nonlinear dynamic systems. The main content of this dissertation include: (1) Fuzzy modeling and synchronization of hyperchaotic systems; (2)Passivity and

controller passification of uncertain fuzzy systems; (3)Stability analysis and H

∞

design of fuzzy large-scale systems; (4)Stability analysis of fuzzy large-scale systems with time delays.

The main originality in this dissertation can be summarized as follows:

1. F uzzy modeling and synchronization study of hyperchaotic systems;

The hyperchaotic systems can produce complex chaotic attractor which has more than one positive Lyapunov exponent. It is important for secure communications to study the hyperchaotic synchronization between hyperchaotic systems. We study the fuzzy modeling for two typical hyperchaotic systems. Based on the T–S fuzzy hyperchaotic models, simpler fuzzy controllers have been designed for synchronizing hyperchaotic systems via the exact linearization techniques.

2.The study of Passivity and passification of uncertain fuzzy systems;

The passivity theory intimately related to the circuit analysis methods has received a lot of attention from the control community since 1970s. There exists a lot of results in nonlinear systems, but the passivity of fuzzy systems has not been fully investigated. T-S fuzzy model provides an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning. So, study on passivity of T-S fuzzy model is conducive to nonlinear control research. We study the passivity and state feedback passification of continuous-time and discrete-timeT-S fuzzy systems with parameter uncertainties respectively.

3.Stability Analysis and H

Controller Design of Fuzzy Large-Scale Systems

∞

One of the foremost challenges to system theory brought forth for present-day technological, environmental and societal process is to overcome the increasing size and complexity of the relevant mathematical models. There were considerable interests in the research of nonlinear large-scale systems in past years. It is very difficult for stability analysis and controller design for nonlinear large-scale systems.