高阶系统方法——Ⅱ.能控性与全驱性  

High-order System Approaches:Ⅱ.Controllability and Full-actuation

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8期1571-1581,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：本文首先简述了基于状态空间模型的一阶动态系统的能控性进展,指出了一阶系统方法中卡尔曼能控性体系的一些问题.然后证明了线性定常系统能控的充要条件是它能化成一个高阶全驱系统,同时还在一定程度上将这一结果推广到非线性系统的情形.基于这一发现,本文定义了一般动态系统的完全能控性,明确其意义在于存在控制律使得闭环系统为一线性定常的高阶系统,并且可以任意配置闭环特征多项式的系数矩阵,同时还指出其多方面相关结论.In this paper,development in controllability of dynamical systems described by first-order state-space models is firstly overviewed briefly,and problems with the controllability theory originally introduced by Kalman are pointed out.It is then proven that a necessary and sufficient condition for a constant linear system to be controllable is that it can be equivalently expressed as a high-order fully-actuated system,and this result is also generalized,in a sense,to the case of nonlinear systems.Based on this discovery,complete-controllability of general dynamical systems is defined.Together with some other important properties,significance of super-controllability is clearly revealed as such that the system can be turned,by a feedback controller,into a high-order constant linear system with the coefficient matrices of the closed-loop eigen-polynomial being arbitrarily assignable.

关 键 词：能控性 完全能控性 高阶系统 全驱系统 能控规范型 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]