摘要
不确定非线性系统的自适应控制理论及其应用越来越受到人们的重视,现在已经是自动控制研究领域中非常活跃的部分。在现代控制理论的研究中,几何方法和Lyapunov稳定性理论是研究此类问题最重要的研究工具。许多研究考虑具有参数和结构不确定性的非线性控制系统的设计和分析。对具有参数不确定性的非线性系统,基于Backstepping方法的自适应控制研究已成为现代控制理论的主要热点之一。然而,目前已有成果大部分针对的是线性系统或者是单输入单输出非线性系统,而对多输入多输出不确定非线性系统的自适应控制问题研究较少,基于输出反馈的多输入多输出不确定非线性系统自适应控制问题研究则更少。
本文研究了一类具有参数化的严格输出反馈形式的多输入多输出非线性系统的自适应控制问题。针对具有不确定参数、受外源信号干扰等情况下的此类受控系统,分别利用Nussbaum增益、高频增益矩阵分解等方法放宽了以往多输入多输出系统中关于高频增益矩阵的假设条件,基于输出反馈,利用Backstepping方法设计了自适应跟踪控制器。并在输出跟踪问题的基础上,进一步研究了此类受控系统的输出机动问题。本文的主要研究成果如下:
一、减弱了以往针对多输入多输出系统要求高频增益矩阵K p(或K pS )正定的假设条件,只需受控系统线性部分高频增益矩阵Bm (或Bm S )为Hurwitz。通过设计状态观测器,实现了对受控系统状态的虚拟估计。利用Backstepping方法,对受控系统设计出了基于输出反馈的自适应控制器,使得跟踪误差能够任意小,且闭环系统所有信号有界。
二、当受控系统线性部分高频增益矩阵Bm的顺序主子式符号已知时,对高频增益矩阵进行所谓的S1 , D1 ,U 1分解,并设计状态观测器,对受控系统状态进行虚拟估计,利用Backstepping方法,给出了基于输出反馈的自适应控制器设计,使得跟踪误差趋近于零,且闭环系统所有信号有界。
三、当受控系统线性部分高频增益矩阵Bm能够转化成为上三角形矩阵或下三角形
The problem of adaptive control and application for uncertain nonlinear systems has attracted increasing attention. In the research of modern control theory, geometric method and the Lyapunov-based stability theory are the most important tools to investigate the problem of the adaptive control for uncertainty nonlinear systems. In the design and synthesis of nonlinear systems with parametric and structural uncertainty, especially with parameter uncertainty, the adaptive control based on Backstepping approach has made a breakthrough and become the highlight in the control theory. However, what the most existing results deal with is the SISO nonlinear systems, the results for MIMO nonlinear uncertain systems are seldom found.
The goal of this paper is to investigate the adaptive control based on output feedback for a class of parametric strict-feedback multi-input multi-output nonlinear systems with parametric uncertainty. For such MIMO nonlinear systems with parametric uncertainty or exogenous signals, the assumptions for the high frequency gain matrix of the systems are relaxed using so-called Nussbaum gain or the factorization of the high frequency gain matrix. Enlightened by the output tracking design, the output maneuvering for such systems is taken into account. The main results in this paper are as follows:
1. Compared to the positive define assumption for the high frequency gain matrix K p (or K pS ) of the MIMO linear systems, in this paper, only the hurwitz is required. The output feedback adaptive controller is presented based on Backstepping method which renders the tracking error arbitrary small and all signals of the closed-loop systems are bounded through the proposed scheme.
2. When the sign of the leading minitor of the high frequency gain matrix Bm is known, the output feedback adaptive controller based on Backstepping method is presented using the so-called S1 , D1 ,U 1 factorization for Bm . The design scheme guarantees that the tracking
引文
[1] 斯洛廷,李卫平.应用非线性控制[M].北京:国防工业出版社.1992
[2] Isidori A.Nonlinear Control Systems[M].Berlin:Springer-Verlag,1995
[3] 杨俊华,吴捷,胡跃明.反步方法原理及在非线性鲁棒控制中的应用[J].控制与决策,2002,17(1):642-653
[4] 冯纯伯,费树岷.非线性控制系统分析与设计[M].北京:电子工业出版社,1998.
[5] Lin W,Pongvuthithum R.Nonsmooth adaptive stabilization of cascade systems with nonlinear parameterization via partial-state feedback[J].IEEE Transactions on Automatic Control,2003,48(10):1809-1816
[6] Dayawansa W,Boothby W M,Elliott D L.Global state and feedback equivalence of nonlinear systems[J].Systems & Control Letters,1985,6:229-234
[7] Hunt L R,Su R,Meyer G.Global transformations of nonlinear systems[J].IEEE Transactions on Automatic Control,1983,28:24-31
[8] Marino R.On the largest feedback linearizable subsystem[J].Systems & Control Letters,1986,6:345-351
[9] Marino R,Boothby W M,Elliot D L.Geometric properties of linearizable control systems[J].Mathematical Systems Theory,1985,18:97-123
[10] Khalil H K.Nonlinear systems[M].New York:Macmillan,1992
[11] Shi X P , Xu T S . Optimal control of two classes of uncertain nonlinear systems[J].Electric Machinesand Control,2000,4(4):223-226
[12] Bartolini G,Pydynowski P.Asymptotic linearization of uncertain nonlinear system by means of continuous control[J].Int.J.Robust Nonlinear Control,1993,3(2):87-103.
[13] 苏宏业,褚健,王 程.多输入非线性系统控制的分步变换与设计[J].控制与决策,1995,10(5):444-449
[14] 薛小平,崔平远.一类多变量非线性系统的解耦控制及线性化[J].哈尔滨工业大学学报,1996,28(2):11-15
[15] Zhen C,Chun Y S.Output tracking control of takagi-sugeno fuzzy systems withapplication to an underactuated robot[J].Proceedings of the 2002 IEEE International Conference on Fuzzy Systems,2002,2:1416-1421
[16] Chen J Y.Hybrid model-based adaptive fuzzy control system[J].Proceedings of the 2002 IEEE International Conference on Fuzzy Systems,2002,2:1126-1131
[17] Golea N,Golea A,Benmahammed K.Fuzzy model reference adaptive control[J ].IEEE Transactions on Fuzzy Systems,2002,10(4):436-444
[18] Shi C,Cheok A C.Performance comparison of fused soft control/hard observer type controller with hard control/hard observer type controller for switched reluctance motors[J].IEEE Transactions on Systems,Man and Cybernetics,2002,32(2):99-112
[19] Hwang C L.Fuzzy linear pulse-transfer function-based sliding-mode control for nonlinear discrete-time systems[J].IEEE Transactions on Fuzzy Systems,2002,10(4):187-197
[20] 孙增圻,张再兴.智能控制理论与技术[M].北京:清华大学出版社.2000
[21] Ren X M,Rad A B,Chan P T,et al.Identification and control of continuous-time nonlinear systems via dynamic neural networks[J].IEEE Transactions on Industrial Electronics,2003,50(6):478- 486
[22] Huang S N,Tan K K,Lee T H.Further results on adaptive control for a class of nonlinear systems using neural networks[J].IEEE Transactions on Neural Networks,2003,14(5):719-722
[23] Li S R,Shi H T,Li F.RBFNN based direct adaptive control of MIMO nonlinear system and its application to a distillation column[J].Proceedings of the 4th World Congress on Intelligent Control and Automation,2002,4 (6):2896-2900
[24] Wai R J . Hybrid fuzzy neural-network control for nonlinear motor-toggle servomechanism[J].IEEE Transactions on Control Systems Technology,2002,10 (7):519 -532
[25] Lin W S,Hung C P.CMAC based integral variable structure control of nonlinear system[J].Proceedings of the 2002 International Joint on Neural Networks,2002,2(5):1183-1188
[26] 龙晓林,蒋静坪.非线性控制及其先进控制策略[J].武汉理工大学学报,2004,26(4):8-13
[27] 陈翰馥,郭雷.现代控制理论的若干进展及展望[J].科学通报,1998,43(1):1-7
[28] Michino R,Mizumoto I,Tao Y,et al.High gain adaptive output feedback control for time-varying nonlinear systems with higher order relative degree[C].Proc.of the 5th Asian Control Conference.2004,2024-2031
[29] Lin W.Adaptive output tracking of inherently nonlinear systems with nonlinear parameterization[J].IEEE Transactions on Automatic Control,2003,48(10):1737-1749
[30] Lin W.Adaptive control of nonlinearly parameterized systems:a nonsmooth feedback framework[J].IEEE Transactions on Automatic Control,2002,47(5):757-774
[31] Ye X D.Global adaptive control of nonlinearly parametrized systems[J].IEEE Transactions on Automatic Control,2003,48(1):169-173
[32] Ding Z T.Adaptive stabilization of a class of nonlinear systems with unstable internal dynamics[J].IEEE Transactions on Automatic Control,2003,48(10):1788-1792
[33] Ge S S,Hong F,Lee T H. Adaptive neural network control of nonlinear systems with unknown time delays[J].IEEE Transactions on Automatic Control,2003,48(11):2004-2010
[34] Marino R,Tomei P.Adaptive output feedback tracking with almost disturbance decoupling for a class of nonlinear systems[J]. Automatica, 2000, 36: 1871-1877
[35] Jiang Z P.Decentralized and adaptive nonlinear tracking of large scale systems via output feedback[J].IEEE Transactions on Automatic Control,2000,45(11):2122-2128
[36] Polycarpou M M ,Ioannou P A.A robust adaptive nonlinear control design [J].Automatica,1995,32:423- 427
[37] Kanellakopolous I,Krstic M,Kokotovic P V,et al.Adaptive control of output- feedback nonlinear systems[C] . Proceedings of the 32nd Conference on Decision and Control.1993.1061-1066
[38] Marino R, Santosuosso G, Tomei P. Robust adaptive observers for nonlinear system with bounded disturbances[J].IEEE Transactions on Automatic Control,2001,46(6):967-972
[39] Ding Z T.Robust adaptive control of nonlinear output-feedback systems under bounded disturbances[C].Proceedings of the 35th Conference on Decision and Control.Kobe,Japan:1996.4753-4758
[40] Serrani A,Isidori A.Semiglobal nonlinear output regulation with adaptive internal model[C]. Proceedings of the 39th IEEE Conference on Decision and Control.Sydney,Australia:2000.1649-1653
[41] Ye X D,Jiang J P.Adaptive nonlinear design without a priori knowledge of control directions[J]. IEEE Transactions on Automatic Control,1998, 43(11):1617-1621
[42] Kanellakopoulos I,Kokotovic P V,Morse A S.Systematic design of adaptive controllers for feedback linearizable systems [J].IEEE Transactions on Automatic Control,1991,36(11):1241-1253
[43] Krstic M,Kanellakopoulos I,Kokotovic P V.Adaptive nonlinear control without over-parameterization[J].Systems & Control Letters,1992,19(3):177-185
[44] Krstic M,Kanellakopoulos I,Kokotovic P V.Nonlinear and Adaptive Control Design[M].New York:A Wiley Interscience Publication,John Wiley and Sons,1995
[45] 高为炳.非线性系统导论[M].北京:科学出版社,1989
[46] Danbing S,Annaswammy A M,Baillieul J.Adaptive control of nonlinear systems with a triagular structure[J].IEEE Transactions on Automatic Control,1994,39 (7):1411 -1427
[47] Skjetne R,Fossen T I,Kokotovic P V.Robust output maneuvering for a class of nonlinear systems[J].Automatica,2004,40:373-383
[48] Krstic M,Kanellakopoulos I,Kokotovic P V.Nonlinear design of adaptive controllers for linear systems[J].IEEE Transactions on Automatic Control,1994,39(4):738 - 752
[49] Jiang Z P,Pomet J B.Combining backstepping and time-varying techniques for a new set of adaptive controllers[C].Proceedings of the 33rd IEEE Conference on Decision and Control.Lake Buena Vista,FL:1994.2207-2212
[50] Jiang Z P,Praly L.Iterative designs of adaptive controllers for systems with nonlinear integrators[C] . Proceedings of the 30rd IEEE Conference on Decision and Control.Brighton,UK:1991.2482-2487
[51] Kanellakopoulos I.Passive adaptive control of nonlinear systems[J].International Journal of Adaptive Control and Signal Processing,1993,7:339-352
[52] Kanellakopoulos I,Krein P T,Disilvestro F.Nonlinear flux-observe-based control of induction motors[C].Proceedings of the 1992 American Control Conference.Chicago,IL:1992.1700-1704
[53] Kanellakopoulos I,Kokotovic P V,Morse A S.Adaptive nonlinear control with incomplete state information[J].International Journal of Adaptive Control and Signal Processing.1992,6:367-394
[54] Kanellakopoulos I,Kokotovic P V,Morse A S.A toolkit for nonlinear feedback design[J].Systems & Control Letters,1992,18:83-92
[55] Kanellakopoulos I, Krstic M,Kokotovic P V.Interlaced controller-observer design for adaptive nonlinear control[C] . Proceedings of the 1992 American Control Conference.Chicago,IL:1992.1337-1342
[56] Seto D,et al. Adaptive control of a class of nonlinear systems with a triangular structure[J].IEEE Transactions on Automatic Control,1992,37:1666-1682
[57] Marino R,Tomei P.Robust stabilization of feedback linearizable time-varying uncertain nonlinear systems[J].Automatica,1993,29:181-189
[58] Ge S S.Advanced control techniques of robtic manipulators[C].Proceedings of American Control Conference,1998
[59] 陈卫田等.一类不确定非线性系统的鲁棒控制[J].控制与决策(增刊),1997,12:524-527
[60] 陈卫田,周绍生等.一类不确定非线性系统的输出反馈控制[J]. 控制理论与应用,1998,15(5)
[61] Kokotovic P V et al.Foundations of adaptive control[M].Berlin:Springer-verag,1991
[62] Bastin G.Adaptive nonlinear control of fed-batch stirred tank reactors[J].International Journal of Adaptive Control and Signal Processing.1992,6:273-284
[63] Ling Y,Tao G.Adaptive backstepping control design for linear multivariable plants[C].Proceedings of the 35th Conference on Decision and Control.Kobe, Japan:1996.3:2438-2443.
[64] Zhang Y , Ioannou . P A . Nonlinear control design for linear time varying systems[C].Proc of the 35th Conference on Decision and Control.Kobe,Japan:1996.3353-3358
[65] Zhang Y,Ioannou.P A.Linear robust adaptive control design using a nonlinear approach[C].Proc of the 13th Triennial World Congress,IFAC.San Francisco:1996.223-228
[66] Nussbaum R D.Some remarks on a conjecture in parameter adaptive control[J].Systems & Control Letters,1983,3:243-246
[67] Ioannou P A,Sun K.Robust Adaptive Control[M].New Jersey:Prentice Hall PTR,1996
[68] Ding Z T.Model reference adaptive control of dynamic output feedback linearisable systems with unknown high frequency gain[J].IEE Proc.Control Theory Appl.,1997,144(5):427-434
[69] Hsu L, Costa R. MIMO direct adaptive control with reduced prior knowledge of the high frequency gain[C] . Proc . of 38th IEEE Conference on Decision and Control.Phoenix,AZ:1999
[70] Ortega R , Herrera A . A solution to the continuous-time adaptive decoupling problem[J].IEEE Transactions on Automatic Control,1994,39(7):1639-1643
[71] 武玉强等.基于 Backstepping 方法的多变量系统自适应控制[J].控制与决策,2001,16(1): 90-92
[72] Hsu L,Costa R,Imai A,Kokotovic P V.Lyapunov based adaptive control of mimo system[C].Proceedings of American Control Conference.Arlington:2001.4808-4813
[73] Imai A K,Costa R R,Liu H,Tao G.Multivariable MRAC using high frequency gain matrix factorization[C] . Proc . of 40th IEEE Conference on Decision and Control.Orlando,Florida,USA:2001.1193-1198
[74] Ortega R,Hsu L,et al.Adaptive control of multivariable systems with reduced prior knowledge[C] . Proceedings of the 40th IEEE Conference on Decision and Control.Orlando,Florida,USA:2001.4198-4203
[75] Marino R,Tomei P.Global adaptive feedback control of nonlinear systems,Part I:Linear parametrization[J].IEEE Transactions on Automatic Control,1993,38(1):17-32
[76] Kanellakopoulos I, Kokotovic P V,Morse A S.Adaptive output feedback control of aclass of nonlinear systems[C].Proceedings of the 30th IEEE Conference on Decision and Control.Brighton,U K:1991
[77] Krstic M, Kokotovic P V.Adaptive nonlinear output-feedback schemes with Marino-Tomei controller[J].IEEE Transactions on Automatic Control,1996,41:274-280
[78] Willems J C,Byrnes C I.Global adaptive stabilization in the absence of information on the sign of high frequency gain[C].Proc.INRIA Conf.Analysis and Optimization of Systems.Nice,France:1984
[79] Mudgett D R,Morse A S.Adaptive stabilization of linear systems with unknown high frequency gains[J].IEEE Transactions on Automatic Control,1985,30(6):549-554
[80] Ilchmann A.Non-Identifier-Based High-Gain Adaptive Control[M].New York:Springer- Verlag,1993
[81] Martensson B.Remarks on adaptive stabilization of first order nonlinear systems [J].Systems & Control Letters,1990,14:1-7
[82] Lozano R,Moctezuma R G.Model reference adaptive control with unknown high frequency gain sign[J].Automatica,1993,29(6):1565-1569
[83] Lozano R,Brogliato B.Adaptive control of a simple nonlinear system without a priori information on the plant parameters[J].IEEE Transactions on Automatic Control,1992,37:30-37
[84] Marino R,Tomei P.Observer-based adaptive stabilization for a class of nonlinear systems[J].Automatica,1992,28:787–793
[85] Ding Z T.Global adaptive output feedback stabilization of nonlinear systems of any relative degree with unknown high-frequency gains[J].IEEE Transactions on Automatic Control,1998,43(10):1442-1446
[86] Ye X D.Adaptive nonlinear output-feedback control with unknown high-frequency gain sign[J].IEEE Transactions on Automatic Control,2001,46(1):112-115
[87] Ding Z T,Ye X D.A flat-zone modification for robust adaptive control of nonlinear output feedback systems with unknown high-frequency gains[J].IEEE Transactions on Automatic Control,2002,358-363
[88] Ding Z T.Universal output regulation for nonlinear systems in output feedback form[C].Proceedings of the 41st IEEE Conference on Decision and Control.Las Vegas,Nevada,USA:2002.3837-3842
[89] Mizumoto D,Michino R, Takahashi M, et al.Adaptive output feedback control of uncertain MIMO nonlinear systems with unknown orders[C].Proc.of the 16th IFAC world Congress.2005
[90] Ye X D . Decentralized adaptive regulation with unknown high-frequency-gain signs[J].IEEE Transactions on Automatic Control,1999,44(11):2072-2076
[91] Al-Hiddabi S,McClamroch N.Tracking and maneuver regulation control for nonlinear nonminimum phase systems:application to fight control[J].IEEE Transactions on Control System Technologies,2002,10(6):780–792
[92] Skjetne R,Fossen T I,Kokotovic P V.Output maneuvering for a class of nonlinear systems[C].Proceedings of the 15th IFAC world congress automatic control.Barcelona,Spain:2002
[93] Skjetne R.The maneuvering problem[D]:[Ph.D. thesis].Trondheim,Norway:Norwegian University of Science & Technology,2005
[94] Skjetne R,Fossen T I,Kokotovic P V.Adaptive maneuvering,with experiments,for a model ship in a marine control laboratory[J].Automatric,2005,41:289-298
[95] Spong M W,Vidyasagar M.Robot Dynamics and Control[M].New York:Wiley,1989
[96] 郑大钟.线性系统理论(第 2 版)[M].北京:清华大学出版社,2002
[97] Popov V M.Hyperstability of control systems[M].New York:Springer-verlag,1973
[98] LaSalle J P.Stability theory for ordinary differential equations[J].Journal of Differential Equations,1968,4:57-65
[99] 武玉强,周颖,臧强.基于高频增益矩阵分解的多变量系统自适应控制[J].系统工程理论与实践,2003,9:90-97
[100] Zhou Y,Wu Y Q,Fei S M.Adaptive Control of Linear Multivariable Systems with High Frequency Gain Matrix Hurwitz[J].Control Theory and Applications,2005,3(3):280-286
[101] Ding Z T.Global output regulation with minimum information of uncertain nonlinearsystems subject to exogenous signals[J].IEE Proc.Control Theory Appl.,2001,148(3):203-208
[102] Hsu L,Cunha J P V S,Costa R R.Model-reference sliding mode control of uncertain multivariable systems[C].Proceedings of the 40th IEEE Conference on Decision and Control.Orlando,Florida,USA:2001.756-761
[103] Sastry S S , Bodson M . Adaptive Control : Stability , convergence and robustness[M].New Jersey:Prentice Hall,Englewood Cliffs,1989
[104] Morse A S.A gain matrix decomposition and some of its applications[J].Systems & Control Letters,1993,21:1-10
[105] Costa R,Hsu L,Imai A,Tao G.Adaptive Backstepping control design for MIMO plants using factorization[C].Proc.of the American Control Conference.Anchorage,Alaska:2002.4601-4606
[106] Isidori A,Byrnes C I.Output regulation of nonlinear systems[J].IEEE Transactions on Automatic Control,1990,35(2):131-140
[107] Huang J , Rugh W J . On a nonlinear multivariable servomechanism problem[J].Automatica,1990,26(6):963-972
[108] Khalil H K.Robust servomechanism output feedback controllers for a class of feedback linearizable systems[J].Automatric,1994,30(10):1587-1599
[109] Khalil H K.Adaptive output feedback control of nonlinear systems represented by input-output models[J].IEEE Transactions on Automatic Control,1996,41(2):177-188
[110] Marino R,Tomei P,Kanellakopoulos I,Kokotovic P V.Adaptive tracking for a class of feedback linearizable systems[J].IEEE Transactions on Automatic Control,1994,39:1314-1319
[111] Freeman R A,Kokotovic P V.Tracking controllers for systems linear in unmeasured states[J].Automatric,1996,32(5):735-746
[112] Serrani A,Isidori A.Global robust output regulation for a class of nonlinear systems[J].Systems & Control Letters,2000,39:133-139
[113] Ding Z T.Global output regulation of uncertain nonlinear systems with exogenous signals[J].Automatica,2001,37:113-119
[114] Ding Z T.Global output regulation with minimum information of uncertain nonlinear systems subject to exogenous signals[C].Proceedings of the 39th IEEE Conference on Decision and Control.Sydney,Australia:2000.1309-1314
[115] Ding Z T.Universal disturbance rejection for nonlinear systems in output feedback form[J].IEEE Transactions on Automatic Control,2003,48(7):1222-1227
[116] Hauser J,Hindman R.Maneuver regulation from trajectory tracking:Feedback linearizable systems[C].Proceedings of the IFAC symposium on nonlinear control systems design.USA:1995.595–600
[117] Hauser J,Hindman R.Aggressive fight maneuvers[C].Proceedings of the 36th IEEE conference in decision and control.USA:1997.4186–4191
[118] Pettersen K Y,Lefeber E.Way-point tracking control of ships[C].Proceedings of the 40th IEEE conference decision and control.USA:2001