高阶系统方法—Ⅱ.能控性与全驱性

段广仁

doi:10.16383/j.aas.c200369

高阶系统方法—Ⅱ.能控性与全驱性

doi: 10.16383/j.aas.c200369

段广仁^1,

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

基金项目:

国家自然科学基金重大项目 61690210

国家自然科学基金重大项目 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

详细信息

作者简介:
段广仁中国科学院院士, 国家杰出青年基金获得者, 长江学者特聘教授, CAA Fellow, IEEE Fellow, IET Fellow. 1989年获哈尔滨工业大学博士学位, 1991年起任哈尔滨工业大学教授, 现为哈尔滨工业大学控制理论与制导技术研究中心主任.主要研究方向为控制系统的参数化设计, 鲁棒控制, 广义系统, 航天器制导与控制. E-mail: g.r.duan@hit.edu.cn

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出版历程
- 收稿日期: 2020-06-15
- 录用日期: 2020-07-15
- 刊出日期: 2020-08-26

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

DUAN Guang-Ren^1
,

1.
Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001

Funds:

the Major Program of National Natural Science Foundation of China 61690210

the Major Program of National Natural Science Foundation of China 61690212

National Natural Science Foundation of China 61333003

the Self-Planned Task of State Key Laboratory of Robotics and System (HIT) SKLRS201716A

More Information

Author Bio:
DUAN Guang-Ren Academician of the Chinese Academy of Sciences, winner of the National Science Fund for Distinguished Young Scholars, Distinguished Professor of Chang Jiang Scholars Program, CAA Fellow, IEEE Fellow and IET Fellow. He received his Ph. D. degree from Harbin Institute of Technology in 1989, and has been professor at Harbin Institute of Technology since 1991. He is currently the director of the Center for Control Theory and Guidance Technology, Harbin Institute of Technology. His research interest covers parametric design of control systems, robust control, descriptor systems, spacecraft guidance and control

摘要

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.
- 能控性 /
- 完全能控性 /
- 高阶系统 /
- 全驱系统 /
- 能控规范型
Abstract: In this paper, development in controllability of dynamical systems described by flrst-order state-space models is flrstly overviewed briefly, and problems with the controllability theory originally introduced by Kalman are pointed out. It is then proven that a necessary and su–cient 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 deflned. Together with some other important properties, signiflcance 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 coe–cient matrices of the closed-loop eigen-polynomial being arbitrarily assignable.
- Controllability /
- complete-controllability /
- high-order systems /
- fully-actuated systems /
- controllability canonical forms
Recommended by Associate Editor HE Wei
注释:

1) 本文责任编委贺威

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