几类切换系统的异步控制

发布时间：2018-06-09 11:31

  本文选题：切换系统 + 平均驻留时间　； 参考：《哈尔滨工业大学》2016年博士论文

【摘要】：作为一类重要的混杂系统,切换系统由若干个子系统以及一个协调各子系统之间切换的切换策略构成,在自然科学、工程控制和社会系统等方面有着广泛的应用。近年来,学者们对切换系统进行了深入的研究,取得了许多的研究成果。在对切换系统的控制问题进行研究时,一般假设子系统和控制器同步运行,然而,在实际工程控制中,系统在识别子系统和请求相应的控制器时需要一段时间,控制器的切换相对于子系统的切换存在切换时延,从而产生异步切换。本文对几类切换系统的异步控制问题进行研究,主要内容如下：对带有非线性扰动的离散时间切换系统,利用解分析法直接研究其动力学性质。首先,通过迭代方法得到闭环切换系统的状态解,利用平均驻留时间法对所得状态解进行分析,建立使得闭环切换系统指数稳定的充分条件。其次,基于所得稳定性条件,利用线性矩阵不等式方法,设计状态反馈控制器。最后,给出求解状态反馈控制器增益和最小平均驻留时间的最优控制算法。这种解分析方法没有使用任何李雅普诺夫函数,为切换系统的研究提供了新的思路。对带有非线性扰动的连续时间切换系统,采用平均驻留时间方法,研究其有限时间异步控制问题。基于闭环切换系统的状态解,使用Gronwall-Bellman不等式和平均驻留时间方法,建立使得闭环切换系统有限时间稳定的判定条件。利用线性矩阵不等式法设计相应的状态反馈控制器,并给出求解状态反馈控制器和平均驻留时间的算法。最后,通过具体仿真实例来验证结论的正确性。对带有时变时滞的切换系统,基于模型依赖平均驻留时间方法,研究其异步H∞控制问题。所考虑的时变时滞不仅存在于系统状态而且存在于系统的输出。首先,将传统的加权H∞性能的概念推广到模型依赖平均驻留时间信号下的切换系统中,采用分段李雅普诺夫函数法,建立使得系统指数稳定且具有H∞性能的判定准则。其次,基于所选参数的数值,将子系统分成两类进行研究,设计两类较平均驻留时间小的模型依赖平均驻留时间。最后,设计能够保证闭环系统指数稳定且具有H∞性能的动态输出反馈控制器。给出动态输出反馈控制器和模型依赖平均驻留时间的计算算法,并通过具体仿真实例来验证算法的有效性。
[Abstract]:As an important hybrid system, the switched system is composed of several subsystems and a switching strategy to coordinate the switching between the subsystems. It has been widely used in natural science, engineering control and social systems. In recent years, scholars have carried on the thorough research to the switched system, obtained many research results. When studying the control problem of switching system, it is generally assumed that the subsystem and the controller run synchronously. However, in the actual engineering control, it takes some time for the system to identify the subsystem and request the corresponding controller. The handoff of controller has a handoff delay relative to the handoff of subsystem, which results in asynchronous handoff. In this paper, the asynchronous control problems of several switched systems are studied. The main contents are as follows: for discrete-time switched systems with nonlinear perturbations, the dynamic properties of the switched systems are studied directly by solution analysis. Firstly, the state solution of the closed-loop switched system is obtained by iterative method, and the obtained state solution is analyzed by the mean resident time method, and a sufficient condition for exponential stability of the closed-loop switched system is established. Secondly, based on the obtained stability conditions, a state feedback controller is designed by using linear matrix inequality (LMI) method. Finally, an optimal control algorithm for state feedback controller gain and minimum average dwell time is presented. This method does not use any Lyapunov functions and provides a new idea for the study of switched systems. For continuous-time switched systems with nonlinear perturbations, the finite time asynchronous control problem is studied by using the mean dwell time method. Based on the state solution of the closed-loop switched system, the Gronwall-Bellman inequality and the mean dwell time method are used to establish the criteria for the stability of the closed-loop switched system in finite time. The linear matrix inequality (LMI) method is used to design the corresponding state feedback controller, and an algorithm for solving the state feedback controller and the average dwell time is given. Finally, the correctness of the conclusion is verified by a specific simulation example. For switched systems with time-varying delays, the asynchronous H _ 鈭，

本文编号：1999577