【作者】 李丹丹；

【导师】 王培光；

【作者基本信息】 河北大学 ， 控制理论与控制工程， 2010， 硕士

【摘要】 本论文主要研究了切换系统的最优切换律问题。切换系统是混合动态系统中重要的一类。混合动态系统是由几个连续子系统或者离散子系统以及作用在其中的切换规则所组成的。由于切换的动作,使切换系统的动态特性变得非常复杂,在实际生产生活中,系统切换规则的设计对于切换系统的研究有着十分重要的作用。本文以线性切换系统为例,主要分析了脉冲切换系统的最优切换律问题,研究了基于范数和基于收敛路径的脉冲切换系统的最优切换律的求取,考虑了切换系统切换规则的选择。总体而言,本文主要完成了以下几项研究工作:(1)讨论了线性脉冲切换系统的最优切换律。首先根据系统矩阵束的约束条件,得到线性脉冲切换系统渐近稳定时切换律的取值范围。其次从每次切换后状态点的范数取值逐渐变小的角度,给出了基于范数的最优切换律的分析方法,切换系统渐近稳定的收敛过程中,采用不同的切换律,得到的系统运行结果也不同。最后,通过实例仿真,验证了设计方法的正确性。(2)对一类周期切换线性脉冲切换系统,研究了其在渐近稳定条件下切换系统基于收敛路径的最优切换律。从渐近稳定系统收敛过程中收敛运行的路径最小的角度,给出了基于收敛路径的最优切换律的分析方法。通过仿真实例,验证了设计方法的正确性和有效性。更多还原

【Abstract】 The optimal switching law of switched systems is researched in this article. As an important class of hybrid dynamical systems, the switched system is composed of a family of continuous-time or discrete-time subsystems and a rule orchestrating the switching among the subsystems. Due to the switching signal, its dynamical performance becomes very complicated. Hence, it is very important to choose a property switching law in the practical production.This dissertation investigates how to choose a proper switching law from switching time for the linear switched systems. The main work incules the analysis of the optimal switching laws of impulsive swithed systems and the research on the optimal switching laws based on norm and convergence path, the choosing of switching laws. The main contributions of the research work presented in this dissertation are as follows:(1) The optimal switching law is discussed for the linear impulsive switched systems. Firstly, asymptotically stable value range of the switching law is obtained based on the constraint condition of matrix pencil for the linear impulsive switched system. Secondly, different running results of system are got because of the choosing of switching law, in the asymptotically stable convergence process of switched system. Then, the analysis method of optimal switching law based on the norm is present in the view of the gradually decreased norm value of the state points after the switching. Finally, instance simulation verify the effectiveness of this method.(2) The optimal switching law of switching systems based on the convergence of the optimal switching path in the asymptotic stability conditions is studied for a class of periodic switched linear impulsive switched systems. The analysis of the optimal switching based on the convergence route is present from asymptotically stable convergence process the minimum angle of path of converge operation. The simulation example, verify the correctness and validity of the design method.更多还原