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高阶系统方法—Ⅱ.能控性与全驱性

段广仁

段广仁. 高阶系统方法-Ⅱ.能控性与全驱性. 自动化学报, 2020, 46(8): 1571−1581 doi: 10.16383/j.aas.c200369
引用本文: 段广仁. 高阶系统方法-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 full-actuation. Acta Automatica Sinica, 2020, 46(8): 1571−1581 doi: 10.16383/j.aas.c200369
Citation: Duan Guang-Ren. High-order system approaches: Ⅱ. Controllability and full-actuation. Acta Automatica Sinica, 2020, 46(8): 1571−1581 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
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

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

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: 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.
    Recommended by Associate Editor HE Wei
    1)  本文责任编委  贺威
  • [1] 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. Full-actuated systems and parametric designs. Acta Automatica Sinica, 2020, 46(7): 1333-1345 doi: 10.16383/j.aas.c200234
    [2] 陈云烽.一类非线性系统的能控性条件.控制理论与应用, 1985, 2(2): 114-118 http://www.cnki.com.cn/Article/CJFDTotal-KZLY198502013.htm

    Chen Yun-Feng. A sufficient condition for controllability of a class of nonlinear systems. Control Theory & Applications, 1985, 2(2): 114-118 http://www.cnki.com.cn/Article/CJFDTotal-KZLY198502013.htm
    [3] 陈彭年, 贺建勋.一类控制有约束的非线性系统的全局可控性.控制理论与应用, 1986, 3(2): 94-99 http://www.cnki.com.cn/Article/CJFDTotal-KZLY198602012.htm

    Chen Peng-Nian, He Jian-Xun. Global controllability of a class of nonlinear systems with restrained control. Control Theory & Applications, 1986, 3(2): 94-99 http://www.cnki.com.cn/Article/CJFDTotal-KZLY198602012.htm
    [4] Vidyasagar M. A controllability condition for nonlinear systems. IEEE Transactions on Automatic Control, 1972, 17(4): 569-570 doi: 10.1109/TAC.1972.1100064
    [5] Mirza K, Womack B. Controllability of a class nonlinear systems. IEEE Transactions on Automatic Control, 1972, 16(4): 531-535
    [6] Balachandran K, Somasundaram D. Controllability of nonlinear systems consisting of a bilinear mode with time-varying delays in control. Automatica, 1984, 20(2): 257-258 doi: 10.1016/0005-1098(84)90035-9
    [7] Somasundaram D, Balachandran K. Controllability of nonlinear systems consisting of a bilinear mode with distributed delays in control. IEEE Transactions on Automatic Control, 1984, 29(6): 573-575 doi: 10.1109/TAC.1984.1103583
    [8] Balachandran K, Dauer J P. Controllability of perturbed nonlinear delay systems. IEEE Transactions on Automatic Control, 1987, 32(2): 172-174 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=d6ddadd1122a769d6182f0779de53bd2
    [9] Klamka J. On the local controllability of perturbed nonlinear systems. IEEE Transactions on Automatic Control, 1975, 20(2): 289-291 doi: 10.1109/TAC.1975.1100929
    [10] Klamka J. On the global controllability of perturbed nonlinear systems. IEEE Transactions on Automatic Control, 1975, 20(1): 170-172 http://cn.bing.com/academic/profile?id=4e89d00e0ca33e72fa1ccfddb3124007&encoded=0&v=paper_preview&mkt=zh-cn
    [11] Klamka J. Relative controllability of nonlinear systems with delays in control. Automatica, 1976, 12(6): 633-634 doi: 10.1016/0005-1098(76)90046-7
    [12] Klamka J. Controllability of nonlinear systems with delay in control. IEEE Transactions on Automatic Control, 1975, 20(5): 702-704 doi: 10.1109/TAC.1975.1101046
    [13] Sun Y M. Necessary and sufficient condition for global controllability of planar affine nonlinear systems. IEEE Transactions on Automatic Control, 2007, 52(8): 1454-1460 doi: 10.1109/TAC.2007.902750
    [14] Sun Y M. Further results on global controllability of planar nonlinear systems. IEEE Transactions on Automatic Control, 2010, 55(8): 1872-1875 doi: 10.1109/TAC.2010.2048054
    [15] Nam K, Araostathis A. A sufficient condition for local controllability of nonlinear systems along closed orbits. IEEE Transactions on Automatic Control, 1992, 37(3): 378-380 doi: 10.1109/9.119642
    [16] Celikovsky S, Nijmeijer H. On the relation between local controllability and stabilizability for a class of nonlinear systems. IEEE Transactions on Automatic Control, 1997, 42(1): 90-94 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=73132ce6f6c6439719d30dfdf895b228
    [17] Celikovsky S. Local stabilization and controllability of a class of non-triangular nonlinear systems. IEEE Transactions on Automatic Control, 2000, 45(10): 1909-1913 doi: 10.1109/TAC.2000.880997
    [18] Mirza K, Womack B. On the controllability of a class of nonlinear systems. IEEE Transactions on Automatic Control, 1971, 16(5): 497-483 doi: 10.1109/TAC.1971.1099795
    [19] Mirza K, Womack B. On the controllability of nonlinear time-delay systems. IEEE Transactions on Automatic Control, 1972, 17(6): 812-814 doi: 10.1109/TAC.1972.1100155
    [20] 张嗣瀛, 王景才, 刘晓平.微分几何方法与非线性控制系统(5).信息与控制, 1992, 21(5): 288-294 http://www.cnki.com.cn/Article/CJFDTotal-XXYK199205006.htm

    Zhang Si-Ying, Wang Jing-Cai, Liu Xiao-Ping. Differential geometric methods and nonlinear control systems. Information and Control, 1992, 21(5): 288-294 http://www.cnki.com.cn/Article/CJFDTotal-XXYK199205006.htm
    [21] 刘晓平, 张嗣瀛.对称非线性控制系统的能控性.控制理论与应用, 1991, 8(4): 452-455 http://www.cnki.com.cn/Article/CJFDTotal-KZLY199104018.htm

    Liu Xiao-Ping, Zhang Si-Ying. Controllability of nonlinear control systems with symmetries. Control Theory & Applications, 1991, 8(4): 452-455 http://www.cnki.com.cn/Article/CJFDTotal-KZLY199104018.htm
    [22] 刘晓平.对称非线性控制系统的能控分解.控制与决策, 1992, 7(1): 63-66 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=89520

    Liu Xiao-Ping. Controllability decomposition for nonlinear control systems with symmetries. Control and Decision, 1992, 7(1): 63-66 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=89520
    [23] 赵军, 张嗣瀛.关于非线性的对称性、可达性与可控性.控制理论与应用, 1992, 9(2): 148-154 http://www.cnki.com.cn/Article/CJFDTotal-KZLY199202006.htm

    Zhao Jun, Zhang Si-Ying. On symmetries, reachability and controllability of nonlinear systems. Control Theory & Applications, 1992, 9(2): 148-154 http://www.cnki.com.cn/Article/CJFDTotal-KZLY199202006.htm
    [24] 井元伟, 胡三清, 刘晓平, 张嗣瀛.可解的具有广义对称性的非线性系统的同构分解与可控性.控制理论与应用, 1996, 13(2): 259-263

    Jing Yuan-Wei, Hu San-Qing, Liu Xiao-Ping, Zhang Si-Ying. Isomorphic decompositon and controllability of systems possessing solvable general symmetries. Control Theory & Applications, 1996, 13(2): 259-263
    [25] 铁林, 蔡开元, 林岩.双线性系统可控性综述.自动化学报, 2011, 37(9): 1040-1049 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zdhxb201109002

    Tie Lin, Cai Kai-Yuan, Lin Yan. A survey on the controllability of bilinear systems. Acta Automatica Sinica, 2011, 37(9): 1040-1049 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zdhxb201109002
    [26] Bellman R, Bentsman J, Meerkov S. Vibrational control of nonlinear systems: Vibrational controllability and transient behavior. IEEE Transactions on Automatic Control, 1986, 31(8): 717-724 doi: 10.1109/TAC.1986.1104383
    [27] Cortes J, Martinez S, Bullo F. On nonlinear controllability and series expansions for Lagrangian systems with dissipative forces. IEEE Transactions on Automatic Control, 2002, 47(8): 1396-1401 doi: 10.1109/TAC.2002.801187
    [28] Melody J, Basar T, Bullo F. On nonlinear controllability of homogeneous systems linear in control. IEEE Transactions on Automatic Control, 2003, 48(1): 139-143 doi: 10.1109/TAC.2002.806667
    [29] Sunahara Y, Kabeuchi T, Asada Y, Aihara S, Kishino K. On stochastic controllability for nonlinear systems. IEEE Transactions on Automatic Control, 1974, 19(1): 49-54 doi: 10.1109/TAC.1974.1100464
    [30] 贺昌政, 杨柳.非线性控制系统的能控性及在刚体动力学中的应用.控制理论与应用, 2000, 17(2): 204-208 doi: 10.3969/j.issn.1000-8152.2000.02.011

    He Chang-Zheng, Yang Liu. The controllability of nonlinear control system and its application to dynamics of rigid body. Control Theory & Applications, 2000, 17(2): 204-208 doi: 10.3969/j.issn.1000-8152.2000.02.011
    [31] 王晓明, 崔平远, 崔祜涛.仿射非线性系统的能控性.控制与决策, 2008, 23(10): 1129-1134 doi: 10.3321/j.issn:1001-0920.2008.10.010

    Wang Xiao-Ming, Cui Ping-Yuan, Cui Hu-Tao. Controllability of affine nonlinear systems. Control and Decision, 2008, 23(10): 1129-1134 doi: 10.3321/j.issn:1001-0920.2008.10.010
    [32] Bhat S R. Controllability of nonlinear time-varying systems: Applications to spacecraft attitude control using magnetic actuation. IEEE Transactions on Automatic Control, 2005, 50(11): 1725-1735 doi: 10.1109/TAC.2005.858686
    [33] 徐志宇, 许维胜, 余有灵, 吴启迪. DC-DC变换器在恒功率负载下的能控性.控制理论与应用, 2010, 27(9): 1273-1276 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=kzllyyy201009026

    Xu Zhi-Yu, Xu Wei-Sheng, Yu You-Ling, Wu Qi-Di. Controllability of DC-DC converters with constant power-load. Control Theory & Applications, 2010, 27(9): 1273-1276 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=kzllyyy201009026
    [34] Nishimura Y, Tsubakino D. Local controllability of single-input nonlinear systems based on deterministic wiener processes. IEEE Transactions on Automatic Control, 2020, 65(1): 354-360 doi: 10.1109/TAC.2019.2912452
    [35] Muller M A, Liberzon D, Allgower F. Norm-controllability of nonlinear systems. IEEE Transactions on Automatic Control, 2015, 60(7): 1825-1840 doi: 10.1109/TAC.2015.2394953
    [36] Davison E, Silverman L, Varaiya P. Controllability of a class of nonlinear time-variable systems. IEEE Transactions on Automatic Control, 1967, 12(6): 791-792 doi: 10.1109/TAC.1967.1098756
    [37] 周鸿兴, 赵怡.非线性系统的能控性理论.控制理论与应用, 1988, 5(2): 1-14 http://www.cnki.com.cn/Article/CJFDTotal-KZLY198802000.htm

    Zhou Hong-Xing, Zhao Yi. A study of controllability theory of nonlinear systems. Control Theory & Applications, 1988, 5(2): 1-14 http://www.cnki.com.cn/Article/CJFDTotal-KZLY198802000.htm
    [38] 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. Ⅱ. Current trends and prospects. Control Theory & Applications, 1987, 4(2): 1-9 http://www.cnki.com.cn/Article/CJFDTotal-KZLY198702000.htm
    [39] Gershwin S, Jacobson D. A controllability theory for nonlinear systems. IEEE Transactions on Automatic Control, 1971, 16(1): 37-46 doi: 10.1109/TAC.1971.1099624
    [40] 刘成, 冯元琨, 李春文, 杜继宏.基于非线性系统受控因子的能控性分析方法.控制与决策, 1997, 12(S1): 504-507 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK199700345805

    Liu Cheng, Feng Yuan-Kun, Li Chun-Wen, Du Ji-Hong. A method to nonlinear controllability based on its controllable factors. Control and Decision, 1997, 12(S1): 504-507 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK199700345805
    [41] Hanba S. Controllability to the origin implies state-feedback stabilizability for discrete-time nonlinear systems. Automatica, 2017, 76: 49-52 doi: 10.1016/j.automatica.2016.09.046
    [42] 王文涛, 李媛.一类非线性微分代数系统的能控性子分布.控制理论与应用, 2009, 26(10): 1126-1129 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=kzllyyy200910012

    Wang Wen-Tao, Li Yuan. Controllability distributions of a class of nonlinear differential-algebraic systems. Control Theory & Applications, 2009, 26(10): 1126-1129 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=kzllyyy200910012
    [43] 王文涛, 刘晓平, 赵军.非线性奇异系统的能控性子分布.自动化学报, 2004, 30(5): 716-722 http://www.aas.net.cn/article/id/16206

    Wang Wen-Tao, Liu Xiao-Ping, Zhao Jun. Controllability distributions of nonlinear singular systems. Acta Automatica Sinica, 2004, 30(5): 716-722 http://www.aas.net.cn/article/id/16206
    [44] Zheng Y F, Willems J C, Zhang C S. A polynomial approach to nonlinear system controllability. IEEE Transactions on Automatic Control, 2001, 46(11): 1782-1788 doi: 10.1109/9.964691
    [45] 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): 513-523 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): 513-523 http://www.aas.net.cn/article/id/14560
    [46] Casti J L. Recent developments and future perspectives in nonlinear system theory. SIAM Review, 1982, 24(3): 301-331 doi: 10.1137/1024065
    [47] Brocket R W. Asymptotic stability and feedback stabilization. Differential Geometric Control Theory. Boston: Birkhauser, 1983. 181-191
    [48] Kalman R. On the general theory of control systems. IRE Transactions on Automatic Control, 1959, 4(3): 110 doi: 10.1109/TAC.1959.1104873
    [49] Kalman R E. On the general theory of control systems. IFAC Proceedings Volumes, 1960, 1(1): 491-502 doi: 10.1016/S1474-6670(17)70094-8
    [50] 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). Science Press, 2016.
    [51] Duan G R. Analysis and Design of Descriptor Linear Systems. New York, USA: Springer, 2010.
    [52] Duan G R. Generalized Sylvester Equations: Unified Parametric Solutions. Raton: CRC Press, 2015.
    [53] 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
    [54] 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 doi: 10.3321/j.issn:1000-6893.1989.05.007

    Li Wen-Lin, Gao Wei-Bing. Controllability canonical form for nonlinear control systems. Acta Aeronautica ET Astronautica Sinica, 1989, 10(5): 249-258 doi: 10.3321/j.issn:1000-6893.1989.05.007
    [55] 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

    Duan Guang-Ren. Quasi-linear system approaches for flight vehicle control - Part 2: Methods and prospects. Journal of Astronautics, 2020, 41(7): 839-849
    [56] 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

    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
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