高阶系统方法--Ⅲ.能观性与观测器设计  

High-order System Approaches: Ⅲ. Observability and Observer Design

作　　者：段广仁[1] DUAN Guang-Ren(Center for Control Theory and Guidance Technology,Harbin Institute of Technology,Harbin 150001)

机构地区：[1]哈尔滨工业大学控制理论与制导技术研究中心,哈尔滨150001

出　　处：《自动化学报》2020年第9期1885-1895,共11页Acta Automatica Sinica

基　　金：国家自然科学基金重大项目(61690210,61690212);国家自然科学基金(61333003);机器人与系统国家重点实验室自主计划任务(HIT)(SKLRS201716A)资助。

摘　　要：平行于第Ⅰ部分中提出的非线性系统的全驱性概念,本文提出了非线性系统的全量测性概念.首先给出了非线性系统的一种能观规范型,并证明了任何与该类非线性系统能观规范型等价的系统,以及任何能观的线性系统,都等价于一个高阶全量测系统.然后据此提出了一般动态系统的完全能观性定义,同时指出线性系统的完全能观性等同于其通常意义下的能观性.最后提出了非线性全量测系统观测器设计的一种简洁方法.基于这种设计,可以使观测误差系统为线性定常系统,并且可以任意配置其特征多项式的系数矩阵.Parallel to the concept of fully-actuated systems proposed in Part Ⅰ, this paper defines for nonlinear systems the concept of fully-measured systems. Firstly, it is proposed for nonlinear systems an observability canonical form, and proven that an observable linear system, or a nonlinear system in the defined observability canonical form, is equivalent to a high-order fully-measured system. Based on such a fact, complete observability of a dynamical system with an arbitrary order is then defined. As a result, the complete observability of a linear constant system is simply consistent with the observability of the system in the conventional sense. Finally, a very simple approach for observer design of nonlinear fully-measured systems is proposed, with which the observation error system is turned into a linear constant one, with the coefficient matrices of its eigen-polynomial arbitrarily assignable.

关 键 词：能观性 完全能观性 高阶系统 全量测系统 能观规范型 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]