高阶系统方法—Ⅲ.能观性与观测器设计

段广仁

doi:10.16383/j.aas.c200370

高阶系统方法—Ⅲ.能观性与观测器设计

doi: 10.16383/j.aas.c200370

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

计量
- 文章访问数: 1822
- HTML全文浏览量: 443
- PDF下载量: 608
- 被引次数: 0
出版历程
- 收稿日期: 2020-06-15
- 录用日期: 2020-07-15
- 刊出日期: 2020-09-28

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

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: 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.
- 能观性 /
- 完全能观性 /
- 高阶系统 /
- 全量测系统 /
- 能观规范型
Abstract: 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.
- Observability /
- complete observability /
- high-order systems /
- fully-measured systems /
- observability canonical forms
Recommended by Associate Editor HE Wei
注释:

1) 本文责任编委贺威

HTML全文

参考文献(37)

[1]	段广仁.高阶全驱系统方法—Ⅱ.能控性与全驱性.自动化学报, 2020, 46(8): 1571-1581 doi: 10.16383/j.aas.c200369 Duan Guang-Ren. High-order system approaches: Ⅱ. Controllability and fully-actuation. Acta Automatica Sinica, 2020, 46(8): 1571-1581 doi: 10.16383/j.aas.c200369
[2]	Tsinias J, Kitsos C. Observability and state estimation for a class of nonlinear systems. IEEE Transactions on Automatic Control, 2019, 64(6): 2621-2628 doi: 10.1109/TAC.2018.2868458
[3]	Bartosiewicz Z. Local observability of nonlinear positive continuous-time systems. Automatica, 2017, 78: 135-138 doi: 10.1016/j.automatica.2016.12.037
[4]	陈彭年, 韩正之, 张钟俊.仿射非线性系统的动态输出反馈镇定.自动化学报, 1997, 23(3): 338-344 http://www.aas.net.cn/article/id/17038 Chen Peng-Nian, Han Zheng-Zhi, Zhang Zhong-Jun. Dynamic output feedback stabilization of affine nonlinear systems. Acta Automatica Sinica, 1997, 23(3): 338-344 http://www.aas.net.cn/article/id/17038
[5]	韩志涛, 段晓东, 张嗣瀛.非线性大系统的弱能观性.东北大学学报(自然科学版), 2003, 24(12): 1123-1125 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=dbdxxb200312001 Han Zhi-Tao, Duan Xiao-Dong, Zhang Si-Ying. Weak observability of nonlinear large-scale system. Journal of Northeastern University (Natural Science), 2003, 24(12): 1123-1125 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=dbdxxb200312001
[6]	Martinelli A. Nonlinear unknown input observability: Extension of the observability rank condition. IEEE Transactions on Automatic Control, 2019, 64(1): 222-237 http://ieeexplore.ieee.org/document/8270358/
[7]	韩正之, 潘丹杰, 张钟俊.非线性系统的能观性和状态观测器.控制理论与应用, 1990, 7(4): 1-9 http://www.cqvip.com/QK/91549X/19903/314118.html Han Zheng-Zhi, Pan Dan-Jie, Zhang Zhong-Jun. Observability and observers of nonlinear systems. Control Theory & Applications, 1990, 7(4): 1-9 http://www.cqvip.com/QK/91549X/19903/314118.html
[8]	程代展, 秦化淑.非线性系统的几何方法(下)—目前动态与展望.控制理论与应用, 1987, 4(2): 1-9 http://www.cnki.com.cn/Article/CJFDTotal-KZLY198702000.htm Cheng Dai-Zhan, Qin Hua-Shu. Geometric methods for nonlinear systems (Part 2): Current dynamics and prospects. Control Theory & Applications, 1987, 4(2): 1-9 http://www.cnki.com.cn/Article/CJFDTotal-KZLY198702000.htm
[9]	Terrell W J. Local observability of nonlinear differential-algebraic equations (DAEs) from the linearization along a trajectory. IEEE Transactions on Automatic Control, 2001, 46(12): 1947-1950 doi: 10.1109/9.975497
[10]	Hespanha J P, Liberzon D, Angeli D, Sontag E D. Nonlinear norm-observability notions and stability of switched systems. IEEE Transactions on Automatic Control, 2005, 50(2): 154-168 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=814cc96835395d60e85f49c36f590632
[11]	Cai S T, Xiao M Q. Boundary observability of wave equations with nonlinear van der pol type boundary conditions. Automatica, 2018, 98: 350-353 doi: 10.1016/j.automatica.2018.09.008
[12]	程代展, 王洪才.一般非线性系统的Kalman分解.自动化学报, 1989, 15(1): 30-36 http://www.aas.net.cn/article/id/14936 Cheng Dai-Zhan, Wang Hong-Cai. Kalman decomposition of general nonlinear systems. Acta Automatica Sinica, 1989, 15(1): 30-36 http://www.aas.net.cn/article/id/14936
[13]	Lin W, Byrnes C I. Zero-state observability and stability of discrete-time nonlinear systems. Automatica, 1995, 31(2): 269-274 doi: 10.1016/0005-1098(94)00088-Z
[14]	Hanba S. Further results on the uniform observability of discrete-time nonlinear systems. IEEE Transactions on Automatic Control, 2010, 55(4): 1034-1038 doi: 10.1109/TAC.2010.2041983
[15]	Anguelova M, Wennberg B. On analytic and algebraic observability of nonlinear delay systems. Automatica, 2010, 46(4): 682-686 doi: 10.1016/j.automatica.2010.01.031
[16]	Chen Z Y. On observability of nonlinear steady-state generators. Automatica, 2010, 46(10): 1712-1718 doi: 10.1016/j.automatica.2010.06.028
[17]	张敏, 罗安, 沈洪远, 王京.一类非线性系统观测器与算例.控制理论与应用, 2002, 19(4): 541-544 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=kzllyyy200204011 Zhang Min, Luo An, Shen Hong-Yuan, Wang Jing. Observer for a class of nonlinear system and an example. Control Theory & Applications, 2002, 19(4): 541-544 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=kzllyyy200204011
[18]	Shim H, Seo J H. Recursive nonlinear observer design: Beyond the uniform observability. IEEE Transactions on Automatic Control, 2003, 48(2): 294-298 doi: 10.1109/TAC.2002.808485
[19]	韩正之, 郑毓蕃, 张钟俊.非线性系统的一种新标准型(Ⅰ)—观察器型.数学物理学报, 1992, 12(3): 318-324 http://www.cnki.com.cn/Article/CJFDTotal-SXWX199203010.htm Han Zheng-Zhi, Zheng Yu-Fan, Zhang Zhong-Jun. A new standard type of nonlinear system (Ⅰ). Observers. Acta Mathematica Scientia, 1992, 12(3): 318-324 http://www.cnki.com.cn/Article/CJFDTotal-SXWX199203010.htm
[20]	Astolfi D, Possieri C. Design of local observers for autonomous nonlinear systems not in observability canonical form. Automatica, 2019, 103: 443-449 doi: 10.1016/j.automatica.2019.02.030
[21]	Hanba S. On the "uniform" observability of discrete-time nonlinear systems. IEEE Transactions on Automatic Control, 2009, 54(8): 1925-1928 doi: 10.1109/TAC.2009.2023775
[22]	段广仁.飞行器控制的伪线性系统方法—第一部分:综述与问题.宇航学报, 2020, 41(6): 633-646 http://www.cqvip.com/QK/95668X/202006/7102487436.html Duan Guang-Ren. Quasi-linear system approaches for flight vehicle control—Part 1: An overview and problems. Journal of Astronautics, 2020, 41(6): 633-646 http://www.cqvip.com/QK/95668X/202006/7102487436.html
[23]	段广仁.飞行器控制的伪线性系统方法—第二部分:方法与展望.宇航学报, 2020, 41(7): 839-849 http://www.cqvip.com/QK/95668X/202006/7102487436.html Duan Guang-Ren. Quasi-linear system approaches for flight vehicle control—Part 2: Methods and prospects. Journal of Astronautics, 2020, 41(7): 839-849 http://www.cqvip.com/QK/95668X/202006/7102487436.html
[24]	Kalman R. On the general theory of control systems. IRE Transactions on Automatic Control, 1959, 4(3): 110 doi: 10.1109/TAC.1959.1104873
[25]	高为炳, 程勉, 夏小华.非线性控制系统的发展.自动化学报, 1991, 17(5): 513-524 http://www.aas.net.cn/article/id/14560 Gao Wei-Bing, Cheng Mian, Xia Xiao-Hua. The development of nonlinear control systems. Acta Automatica Sinica, 1991, 17(5): 513-524 http://www.aas.net.cn/article/id/14560
[26]	Casti J L. Recent developments and future perspectives in nonlinear system theory. SIAM Review, 1982, 24(3): 301-331 doi: 10.1137/1024065
[27]	Brocket R W. Asymptotic stability and feedback stabilization. Differential Geometric Control Theory. Boston: Birkhauser, 1983. 112-121
[28]	韩正之, 刘建华, 郑毅, 张钟俊.非线性控制系统的特性(Ⅰ).控制与决策, 1994, 9(4): 315-320 http://www.cnki.com.cn/Article/CJFDTotal-KZYC404.015.htm Han Zheng-Zhi, Liu Jian-Hua, Zheng Yi, Zhang Zhong-Jun. Characters of nonlinear control systems (Ⅰ). Control and Decision, 1994, 9(4): 315-320 http://www.cnki.com.cn/Article/CJFDTotal-KZYC404.015.htm
[29]	李文林, 高为炳.非线性控制系统的可控标准型问题.航空学报, 1989, 10(5): 249-258 http://www.cnki.com.cn/Article/CJFDTotal-HKXB198905006.htm Li Wen-Lin, Gao Wei-Bing. Controllability canonical form for nonlinear control systems. Acta Aeronautica ET Astronautica Sinica, 1989, 10(5): 249-258 http://www.cnki.com.cn/Article/CJFDTotal-HKXB198905006.htm
[30]	段广仁.线性系统理论(上下册).第3版.北京:科学出版社, 2016. Duan Guang-Ren. Linear System Theory(two volumes) (Third edition). Beijing: Science Press, 2016.
[31]	Duan G R, Gao Y J. State-space realization and generalized Popov Belevitch Hautus criterion for high-order linear systems—The singular case. International Journal of Control, Automation and Systems, 2020, 18(8): 2038-2047 doi: 10.1007/s12555-019-0212-4
[32]	Duan G R. Analysis and Design of Descriptor Linear Systems. New York, USA: Springer, 2010.
[33]	Duan G R. Solution to matrix equation AV + BW = EVF and eigenstructure assignment for descriptor systems. Automatica, 1992, 28(3): 639-643 doi: 10.1016/0005-1098(92)90191-H
[34]	Duan G R, Patton R J. Eigenstructure assignment in descriptor systems via state feedback—A new complete parametric approach. International Journal of Systems Science, 1998, 29(2): 167-178 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=10.1080/00207729808929509
[35]	Duan G R. Eigenstructure assignment and response analysis in descriptor linear systems with state feedback control. International Journal of Control, 1998, 69(5): 663-694 doi: 10.1080/002071798222622
[36]	Duan G R. Parametric eigenstructure assignment in second-order descriptor linear systems. IEEE Transactions on Automatic Control, 2004, 49(10): 1789-1795 doi: 10.1109/TAC.2004.835580
[37]	段广仁.高阶系统方法—Ⅰ.全驱系统与参数化设计.自动化学报, 2020, 46(7): 1333-1345 doi: 10.16383/j.aas.c200234 Duan Guang-Ren. High-order system approaches: Ⅰ. Fully-actuated systems and parametric design. Acta Automatica Sinica, 2020, 46(7): 1333-1345 doi: 10.16383/j.aas.c200234