非线性系统自适应观测器设计研究
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摘要
近年来,非线性观测器设计问题已经成为众多学者关注的研究课题之一,并取得了丰硕的成果.但大多是针对Lipschitz非线性系统状态观测器进行研究的.研究表明,在许多情况下用已有判据来设计Lipschitz非线性系统观测器是无法达到渐进稳定的.本文针对几类不同的非线性系统分别研究了全维,降维及输出带有非线性项的自适应观测器的设计.主要研究结果如下：
·在自适应观测器参数上界已知的情况下,用拟单边Lipschitz条件代替通常的Lipschitz条件研究了一类非线性系统全维,降维自适应观测器的设计.
·对已有系统进行改进,使输出带有非线性项并设计其观测器.
·在自适应观测器参数上界未知的情况下,设计自适应调节器来估计未知参数范数.并用拟单边Lipschitz条件代替通常的Lipschitz条件研究非线性系统的全维,降维自适应观测器设计.
Recently, the non-linear observer design question is one of the research issue paid much attention by many scholars. That researches are made successful and most of them are aimed at Lipschitz non-linear-system state design. Studies have shown that in many cases the existing methods used to design Lipschitz nonlinear systems observer asymptotic stability can not be achieved.
In this paper, different types of nonlinear systems are the-full-order, reduced-order and output whit a nonlinear item adaptive design. Major findings are as follow:
In the situation of know the upper bound of adaptive observer parameters, use quasi-one-sided Lipschitz condition replace the usual condition, research for a class of Lipschitz nonlinear systems with full-order, reduced-order adaptive observe design.
Improvement of existing systems, so that the output with a nonlinear term and to design the observer.
Adaptive observer parameters in the upper bound of the unknown cases, adap-tive regulator design to estimate the unknown parameters of the norm. Quasi-one-sided Lipschitz condition to be replaced with the usual conditions of Lipschitz nonlinear systems with the-full-order, reduced-order is only observed adaptation design.
·在自适应观测器参数上界已知的情况下,用拟单边Lipschitz条件代替通常的Lipschitz条件研究了一类非线性系统全维,降维自适应观测器的设计.
·对已有系统进行改进,使输出带有非线性项并设计其观测器.
·在自适应观测器参数上界未知的情况下,设计自适应调节器来估计未知参数范数.并用拟单边Lipschitz条件代替通常的Lipschitz条件研究非线性系统的全维,降维自适应观测器设计.
Recently, the non-linear observer design question is one of the research issue paid much attention by many scholars. That researches are made successful and most of them are aimed at Lipschitz non-linear-system state design. Studies have shown that in many cases the existing methods used to design Lipschitz nonlinear systems observer asymptotic stability can not be achieved.
In this paper, different types of nonlinear systems are the-full-order, reduced-order and output whit a nonlinear item adaptive design. Major findings are as follow:
In the situation of know the upper bound of adaptive observer parameters, use quasi-one-sided Lipschitz condition replace the usual condition, research for a class of Lipschitz nonlinear systems with full-order, reduced-order adaptive observe design.
Improvement of existing systems, so that the output with a nonlinear term and to design the observer.
Adaptive observer parameters in the upper bound of the unknown cases, adap-tive regulator design to estimate the unknown parameters of the norm. Quasi-one-sided Lipschitz condition to be replaced with the usual conditions of Lipschitz nonlinear systems with the-full-order, reduced-order is only observed adaptation design.
引文
1 Kalman R. E. On a new approach to filtering and prediction problems. Transac tions of the ASME Journal of Basic Engineering. 1960,82(D):35-45
2 Jazw inski A H. Stochastic processes and filering theory. New York:Academic press.1970
3 Oisiovici R M, Cruz S L. State estimation of batch distillation columns using an Extended Kalman filter. Chemical Engineering Sicence.2000,55:4667-4680
4 Kalman R. E.On, a new approach to filtering and prediction problems. Transac tions of the ASME Journal of Basic Engineering.1960,82(D):35-45
5 Reif K, Sonnemann F, Unbehauen R. An EKFBased nonlinear observer with a prescribed degree of stability. Automatic.1998,34(9):1119-1123
6 David G. An introduction to observers. IEEE Transactions on Automatic Con trol.1971,16(6):596-602
7 Arcak M, Kokotovic P. Nonlinear observers:a circle criterion design and ro bustness analysis. Automatica.2001,37(12):1923-1930
8 Rajamani R. Observers for Lipschitz nonlinear systems.IEEE Transactions on Automatic Control.1998,43(3):397-401
9 Cho Y. M, Rajamani R. A systematic approach to adaptive observer synthesis for nonlinear systems. IEEE Transactions on Automatic Control.1997,42(4): 534-537
10 Kreisselmelmeier G, Engel R. Nonlinear observers for autonomous Lipschitz continuous systems. IEEE Trans on Automatic Control.2003,48(3):451-464
11 David G. An introduction to observers. IEEE Transactions on Automatic Con trol.1971,16(6):596-602
12 Liu Y G, Zhang J F. Reduced-order observer-based control design for stochastic nonlinear systems..Systems & Control Letters.2004,52(2):123-135
13 Marino R, Tomei P. Global adaptive observers for nonlinear systems via filtered transformations.IEEE Trans on Automatic Control.1992,37(8):1239-1245
14 Marino R. Adaptive observers for single-output non-Linear systems.IEEE Trans actions on Automatic Control.1990,35(9):1054-1058
15 Gauthierm J. P., Hammonuri M., Othman S. A simple observer for nonlinear systems application to bioreactor. IEEE Transactions on Automatic Control. 1992,37(6):875-879
16 Ciccarella G., Mora M. D., Germani A. A Luenberger-like observer for non-linear Systems.International Journal Control.1993,57(3):537-556
17 Besancon R. Remarks on nonlinear adaptive observer design. Systems & Con-trol Letters.2000,41:271-280
18 Busaw on K. K, Saif M. An observer for a class of disturbance driven nonlinear systems. Appl Math Lett.1998,1(6):109-113
19 Alvarez J. Nonlinear state estimation with robust convergence. Journal of Pro cess Control.2000,10:59-72
20 Corless M, Tu J. State and input estimation for a class of uncertain systems. Automatic.1998,34(6):757-764
21 Ding Yuqin,Liu Yungang.Nonlinear adaptive observer design without a priori knowledge on the unknown parameters. Control Theory & Applications.2008, 25(1):27-32
22朱芳来,韩正之.Lipschitz非线性系统自适应观测器设计.2003,37(6)：943-946
23贺乃宝,姜长生.基于Lyapunov方法的非线性系统自适应观测器设计.南京航空航天大学学报.2006,38(3)：267-270
24 Rajamani R, Cho Y M. Existence and design of observers for nonlinear sys terns:relation to distance to unobservability. International Journal of Control. 1998,69(5):717-731
25 Bestle D, Zeitz M. Canonical form observer design for non-linear time-variable systems. International Journal Control.1983,38(2):419-413
26 Raghavan S, Hedrick J K. Observer design for a class of nonlinear systems. In ternational Journal of Control.1994,59(2); 515-528
27 Zeitz M. The extended Luenberger observers for nonlinear systems. Systems & Control letters.1987,9:149-156
28 Krener A, Isidori A. Linearization by output injection and nonlinear obsrevers. Systems & Control letters.1983,3:47-52
29 Krener A, Respondek W. Nonlinear observers with linearizable error dynamics. SIMA J Control and Optimization.1985,23(2):197-216
30 Besancon G, Hammouri H. On uniform observation of nonuniformly observable systems. Systems and Control Letters.1996,29:9-19
31 Luders G, NarendRa K. S. An adaptive observer and identifier for linear system. IEEE Trans on Automatic Control.1973,18(5):496-499
32 Luders G, Narendra K. S. An new canonical form, for an adaptive observer. IEEE Trans on Automatic Control.1974,19(2):117-119
33 Kreisselmeier G. Adaptive observer with exponential rate of convergence. IEEE Trans on Automatic Control.1973,18(5):428-435
34 Carroll R L, Lindorff D. P. An adaptive observer for single-input single-output linear systems. IEEE Trans on Automatic Control.1973,18(5):428-435
35 Bestin G, Gevers M. R. Stable adaptive observers for nonlinear time-varying systems. IEEE Transactions on Automatic Control.1988,33(7):650-658
36 Besancon G, Morales J. L, Guevrar O H. On adaptive observers for state affine systems and application to synchronous machines. Proc of the 42nd IEEE Conf on Decision and Control. Maui, Hawaii USA:IEEE press.2003:2192-2197
37 Hu G. D. Observers for one-sided Lipschitz non-linear systems. IMA J. Math. Control Inf.2006,23,395-401
38 Hu G. D. A note on observer for one-sided Lipschitz nonlinear systems. IMA J. Math. Control Inf.2008,25,297-303
39 Xu Mingyue. Reduced-order, observer design for one-sided Lipschitz non-linear systems. IMA Journal of Mathematical Control and Information.2009,26, 299-317
40郑大钟.线性系统理论.清华大学出版社,2002：53-78
41 F. E. Thau. Observing the state of nonlinear dynamic systems. Int. J. Contr. 1973,17(3):471-479
2 Jazw inski A H. Stochastic processes and filering theory. New York:Academic press.1970
3 Oisiovici R M, Cruz S L. State estimation of batch distillation columns using an Extended Kalman filter. Chemical Engineering Sicence.2000,55:4667-4680
4 Kalman R. E.On, a new approach to filtering and prediction problems. Transac tions of the ASME Journal of Basic Engineering.1960,82(D):35-45
5 Reif K, Sonnemann F, Unbehauen R. An EKFBased nonlinear observer with a prescribed degree of stability. Automatic.1998,34(9):1119-1123
6 David G. An introduction to observers. IEEE Transactions on Automatic Con trol.1971,16(6):596-602
7 Arcak M, Kokotovic P. Nonlinear observers:a circle criterion design and ro bustness analysis. Automatica.2001,37(12):1923-1930
8 Rajamani R. Observers for Lipschitz nonlinear systems.IEEE Transactions on Automatic Control.1998,43(3):397-401
9 Cho Y. M, Rajamani R. A systematic approach to adaptive observer synthesis for nonlinear systems. IEEE Transactions on Automatic Control.1997,42(4): 534-537
10 Kreisselmelmeier G, Engel R. Nonlinear observers for autonomous Lipschitz continuous systems. IEEE Trans on Automatic Control.2003,48(3):451-464
11 David G. An introduction to observers. IEEE Transactions on Automatic Con trol.1971,16(6):596-602
12 Liu Y G, Zhang J F. Reduced-order observer-based control design for stochastic nonlinear systems..Systems & Control Letters.2004,52(2):123-135
13 Marino R, Tomei P. Global adaptive observers for nonlinear systems via filtered transformations.IEEE Trans on Automatic Control.1992,37(8):1239-1245
14 Marino R. Adaptive observers for single-output non-Linear systems.IEEE Trans actions on Automatic Control.1990,35(9):1054-1058
15 Gauthierm J. P., Hammonuri M., Othman S. A simple observer for nonlinear systems application to bioreactor. IEEE Transactions on Automatic Control. 1992,37(6):875-879
16 Ciccarella G., Mora M. D., Germani A. A Luenberger-like observer for non-linear Systems.International Journal Control.1993,57(3):537-556
17 Besancon R. Remarks on nonlinear adaptive observer design. Systems & Con-trol Letters.2000,41:271-280
18 Busaw on K. K, Saif M. An observer for a class of disturbance driven nonlinear systems. Appl Math Lett.1998,1(6):109-113
19 Alvarez J. Nonlinear state estimation with robust convergence. Journal of Pro cess Control.2000,10:59-72
20 Corless M, Tu J. State and input estimation for a class of uncertain systems. Automatic.1998,34(6):757-764
21 Ding Yuqin,Liu Yungang.Nonlinear adaptive observer design without a priori knowledge on the unknown parameters. Control Theory & Applications.2008, 25(1):27-32
22朱芳来,韩正之.Lipschitz非线性系统自适应观测器设计.2003,37(6)：943-946
23贺乃宝,姜长生.基于Lyapunov方法的非线性系统自适应观测器设计.南京航空航天大学学报.2006,38(3)：267-270
24 Rajamani R, Cho Y M. Existence and design of observers for nonlinear sys terns:relation to distance to unobservability. International Journal of Control. 1998,69(5):717-731
25 Bestle D, Zeitz M. Canonical form observer design for non-linear time-variable systems. International Journal Control.1983,38(2):419-413
26 Raghavan S, Hedrick J K. Observer design for a class of nonlinear systems. In ternational Journal of Control.1994,59(2); 515-528
27 Zeitz M. The extended Luenberger observers for nonlinear systems. Systems & Control letters.1987,9:149-156
28 Krener A, Isidori A. Linearization by output injection and nonlinear obsrevers. Systems & Control letters.1983,3:47-52
29 Krener A, Respondek W. Nonlinear observers with linearizable error dynamics. SIMA J Control and Optimization.1985,23(2):197-216
30 Besancon G, Hammouri H. On uniform observation of nonuniformly observable systems. Systems and Control Letters.1996,29:9-19
31 Luders G, NarendRa K. S. An adaptive observer and identifier for linear system. IEEE Trans on Automatic Control.1973,18(5):496-499
32 Luders G, Narendra K. S. An new canonical form, for an adaptive observer. IEEE Trans on Automatic Control.1974,19(2):117-119
33 Kreisselmeier G. Adaptive observer with exponential rate of convergence. IEEE Trans on Automatic Control.1973,18(5):428-435
34 Carroll R L, Lindorff D. P. An adaptive observer for single-input single-output linear systems. IEEE Trans on Automatic Control.1973,18(5):428-435
35 Bestin G, Gevers M. R. Stable adaptive observers for nonlinear time-varying systems. IEEE Transactions on Automatic Control.1988,33(7):650-658
36 Besancon G, Morales J. L, Guevrar O H. On adaptive observers for state affine systems and application to synchronous machines. Proc of the 42nd IEEE Conf on Decision and Control. Maui, Hawaii USA:IEEE press.2003:2192-2197
37 Hu G. D. Observers for one-sided Lipschitz non-linear systems. IMA J. Math. Control Inf.2006,23,395-401
38 Hu G. D. A note on observer for one-sided Lipschitz nonlinear systems. IMA J. Math. Control Inf.2008,25,297-303
39 Xu Mingyue. Reduced-order, observer design for one-sided Lipschitz non-linear systems. IMA Journal of Mathematical Control and Information.2009,26, 299-317
40郑大钟.线性系统理论.清华大学出版社,2002：53-78
41 F. E. Thau. Observing the state of nonlinear dynamic systems. Int. J. Contr. 1973,17(3):471-479