基于MDADT方法的受限切换系统的镇定问题研究

发布时间：2018-08-30 15:42

【摘要】：作为一类特殊的混杂系统,切换系统是研究混杂系统理论的一种重要模型。切换系统是由一系列连续时间或者离散时间子系统及一条作用在其中的切换规则组成的。由于切换的存在,系统的动态行为会变得十分复杂,从而为切换系统及相关领域提供了很多具有研究价值的课题。另外,实际系统由于存在着生产设备本身物理极限的问题而具有状态受限,因此研究具有状态约束的切换系统就更加具有实际意义。同时,线性切换正系统在网络拥塞控制、传染病控制等领域的广泛应用也引起了众多学者的关注。本论文的主要研究内容如下:本文首先介绍切换系统、切换正系统以及具有状态约束的切换系统的概念。其中包括切换系统的研究背景、主要研究问题以及主要研究方法。在此基础上,从连续时间和离散时间的角度,分别研究具有状态约束的切换系统的镇定问题。针对系统饱和发生与饱和不发生时每一个子系统所对应的Lyapunov函数的衰减率都不相同的特点,提出一种同时具有饱和依赖型和模型依赖型的平均驻留时间方法。另外,给出切换系统的稳定与镇定的充分条件并且设计状态反馈控制器。此外,本文设计的这种模型依赖型的改进的平均驻留时间比标准的平均驻留时间要小,且与饱和依赖型的改进的平均驻留时间方法相比,在一定程度上降低了保守性。然后,研究具有状态约束的连续时间切换正系统镇定问题。首先给出连续时间切换正系统的数学模型,利用前面提出的同时具有饱和依赖型和模型依赖型的改进的平均驻留时间方法,通过推导证明得到了切换正系统镇定的充分条件以及相应的状态反馈控制器。最后,通过数值仿真例子来说明本章所提出方法的有效性。最后,对本文所做的研究工作进行总结并探讨接下来需要继续深入研究的问题,即对未来工作的展望。
[Abstract]:As a special class of hybrid systems, switched systems are an important model to study the theory of hybrid systems. Switched systems are composed of a series of continuous-time or discrete time subsystems and a switching rule acting on them. Because of the existence of handoff, the dynamic behavior of the system will become very complex, which provides a lot of valuable research topics for switched systems and related fields. In addition, the actual system has the state limitation because of the physical limit of the production equipment itself, so it is more meaningful to study the switching system with state constraints. At the same time, the extensive application of linear switched forward system in network congestion control, infectious disease control and other fields has attracted many scholars' attention. The main contents of this thesis are as follows: firstly, the concepts of switched systems, switched positive systems and switched systems with state constraints are introduced. It includes the research background, the main research problems and the main research methods of switched systems. On this basis, the stabilization problem of switched systems with state constraints is studied from the point of view of continuous time and discrete time respectively. In view of the fact that the attenuation rate of Lyapunov functions corresponding to each subsystem is different when saturation occurs and does not occur, an average resident time method with both saturation-dependent and model-dependent is proposed. In addition, sufficient conditions for stability and stabilization of switched systems are given and a state feedback controller is designed. In addition, the improved average residence time of the model dependent type is smaller than that of the standard one, and compared with the improved average residence time method of the saturated dependent type, it reduces the conservatism to some extent. Then, the stabilization problem of continuous-time switched positive systems with state constraints is studied. Firstly, the mathematical model of continuous time switching positive system is given, and the improved average dwell time method with both saturation and model dependence is used. The sufficient conditions for stabilization of switched positive systems and the corresponding state feedback controllers are proved by derivation. Finally, numerical simulation examples are given to illustrate the effectiveness of the proposed method. Finally, the research work done in this paper is summarized and the problems that need to be further studied are discussed, that is, the prospect of future work.
【学位授予单位】：东北电力大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13

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