离散时间状态可观测控制系统的稳定性和同步性

发布时间：2019-06-21 21:39

【摘要】：随着信息时代的发展,现实生活中的许多实际模型可以用复杂网络上的系统来刻画。此外,为了更精确地描述自然界的一些现象,随机因素和时间延迟应该被考虑。因此,研究复杂网络上带有延迟的随机系统动力学行为十分有意义。最近,许多学者研究了复杂网络上随机延迟系统的动力学行为,其中控制方法是一种十分有效的策略。然而,从控制学角度来看,控制成本以及效率等因素也应该被考虑。本文设计了一种不同于连续时间的控制器,即离散时间状态可观测的反馈控制器。主要使用随机分析技巧、图理论知识和Lyapunov方法相结合的方法,研究了复杂网络上带有离散时间状态可观测反馈控制的随机系统稳定性和同步性。本文的第二章,通过设计一种基于离散时间状态可观测的反馈控制器,研究复杂网络上带有时间延迟的随机系统稳定性。本文使用的方法是Lyapunov方法和图理论中的Kirchhoff矩阵数定理,并且给出三个充分性准则,主要包括渐近稳定性和均方渐近稳定性。为了说明该理论具有实际应用价值,本文将新颖的结果应用到复杂网络上的耦合振子系统中。随后,给出一个数值算例及其数值仿真。本文的第三章,通过设计基于离散时间状态可观测的反馈控制器,讨论了复杂网络上随机系统不同类型的同步性,使用Lyapunov方法和图理论中的Kirchhoff矩阵数定理,得到三个充分性准则,主要包括均方同步和均方渐近同步,而且得到两个连续时间状态之间观测时间的一个上界。随后,本文研究了微电网模型的渐近同步性并给出了判定微电网模型均方渐近同步的一个充分性准则。最后,给出了一个数值算例及其数值仿真。
[Abstract]:With the development of information age, many practical models in real life can be described by systems on complex networks. In addition, in order to describe some phenomena in nature more accurately, random factors and time delays should be taken into account. Therefore, it is very meaningful to study the dynamic behavior of stochastic systems with delays on complex networks. Recently, many scholars have studied the dynamic behavior of stochastic delay systems on complex networks, in which the control method is a very effective strategy. However, from the point of view of control science, the factors such as cost control and efficiency should also be considered. In this paper, a feedback controller is designed, which is different from continuous time, that is, discrete time observable feedback controller. In this paper, the stability and synchronization of stochastic systems with discrete time state observable feedback control on complex networks are studied by using stochastic analysis technique, graph theory and Lyapunov method. In the second chapter, the stability of stochastic systems with time delay on complex networks is studied by designing a feedback controller based on discrete time state observability. The method used in this paper is Lyapunov method and Kirchhoff matrix number theorem in graph theory, and three sufficient criteria are given, including asymptotic stability and mean square asymptotic stability. In order to show that the theory has practical application value, the novel results are applied to the coupled oscillator system on complex networks. Then, a numerical example and its numerical simulation are given. In the third chapter, by designing a feedback controller based on discrete time state observability, the synchronization of different types of stochastic systems on complex networks is discussed. Using Lyapunov method and Kirchhoff matrix number theorem in graph theory, three sufficient criteria are obtained, including mean square synchronization and mean square asymptotic synchronization, and an upper bound of observation time between two continuous time states is obtained. Then, the asymptotic synchronization of the microgrid model is studied and a sufficient criterion for determining the mean square asymptotic synchronization of the microgrid model is given. Finally, a numerical example and its numerical simulation are given.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O231

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