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摘要切换系统是一类形式简单、应用广泛的混杂动态系统,有很强的理论研究意义和实际应用背景。本课题先阐述了其研究现状，对切换系统的状态估算问题进行了研究。首先概述了代数估算方法的基本原理，其次介绍了广义函数理论的基本概念和滑动窗口积分的方法。在此基础上，研究了子系统为线性系统（线性定常及线性时变）的切换系统状态估算法，针对文献[1]中切换时刻的估算方法深入研究，并进行了改进。针对子系统为非线性系统的一类切换系统的状态估算问题，我们提出了将非线性系统线性化，转化为文献[25]中线性时变系统模型的形式，接着采用文献[25]中介绍的方法来估算切换系统的切换时刻。最后本课题对基于代数方法的切换系统状态估算研究方向做出展望。6502
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关键词 切换系统 混杂动态系统 代数方法 状态估算 非线性系统
毕业设计说明书（论文）外文摘要
Title State estimation of switched systems based on algebraic methods
Abstract
The switched system is a class of hybrid dynamical system which has a simple form and a wide range of applications, and it has strong theoretical significance and practical application’s background. After elaborating the research status of the hybrid system, this topic discusses the state estimation’s problem of the switched system. First of all, this paper outlines the basic principles of estimation with an algebraic method. Secondly, it introduces the basic concept of the generalized function theory and the method of the sliding window integral. On this basis, we study the state estimation of a switched system which subsystem is a linear system (linear time-invariant system and linear time-variant system). Aim at the estimation method of the switching time in reference [1], we conduct a careful study and improve the algorithm. In order to solve the state estimation’s problem of a switched system which subsystem is a nonlinear system, we propose a linearization for the nonlinear system so that we can turn it into a linear time-varying system model in reference [25]. And then we use the method introduced in reference [25] to estimate the switching time of a switched system. At last, this paper discusses the research’s future direction and the development prospects of the switched system’s state estimation which is based on the algebraic method.
Keywords switched system hybrid system algebraic method state estimation nonlinear system
目 次
1 引言 1
1.1 研究背景 1
1.2 基于代数方法的切换系统状态估算 4
1.2.1 切换系统的研究概况 4
1.2.2 代数方法在线性系统的状态估算中的应用及研究现状 6
1.3 本文工作安排 7
2 代数估计算法原理 9
2.1 切换系统的代数方法估算的基本原理 9
2.2 广义函数理论基础 9
2.3 存在于两子系统间的切换时刻的估算 10
3 切换系统切换时刻的代数估计算法 14
3.1 滑动窗口积分 14
3.2 Q个子系统的系统切换 15
3.3 辨识切换时刻的数值算法 15
4 含有非线性子系统的切换系统的状态观测 19
4.1 非线性系统的基本研究状况 19
4.2 非线性系统状态观测器设计的基本概况 19
4.3 非线性系统的局部线性化的方法 20