基于后推法的不确定非线性系统的自适应神经网络控制
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摘要
近年来,对于非线性系统的控制设计的理论研究及其应用有了很大的发展,并取得了大量的研究成果.但由于现代的工程控制系统大都比较复杂,加上建模误差、参数时滞、未知参数、未建模动态、外界干扰等不确定性,使得现代控制理论中的许多结果在实际应用中不尽人意,因此不确定非线性系统的研究一直是人们研究的热点和难点.
自适应理论作为一种不确定非线性控制策略,特别适用于控制复杂的不确定非线性系统.最近几年,随着非线性backstepping自适应技术和神经网络的发展,在不确定非线性控制系统的设计和分析中,基于backstepping方法的自适应神经网络控制问题,已引起人们的广泛关注,并成为神经网络控制领域中的一个新的研究方向.本文就此领域的相关问题展开研究.本人基于Lyapunov稳定性理论和backstepping方法以及神经网络控制理论,对一类单输入单输出不确定非线性的系统,提出了一种自适应神经网络backstepping控制方法.
论文共包括五部分内容：
第一章：介绍了所研究课题的背景知识,综述了非线性不确定系统自适应控制的研究现状和研究目的意义.
第二章：介绍论文所涉及的基础理论,包括基本概念、主要定理、引理和重要方法.如Lyapunov稳定性理论,backstepping设计方法等,以及几个论文中多次用到的不等式.
第三章：研究了一类单输入单输出不确定非线性系统,采用backstepping方法,设计了自适应神经网络控制器,实现了系统所有信号的有界以及跟踪误差的尽可能小.
第四章：研究了一类具有控制方向的不确定非线性系统的,利用神经网络逼近原理,backstepping控制方法及Lyapunov稳定性理论,设计了自适应神经网控制器,实现了系统所有信号的有界以及跟踪误差的尽可能小.
第五章：对全文进行了总结,并提出下一步研究的方向.
In the recent years, it has developed greatly in the control theory research and application of control design for nonlinear systems, and people have gained tremendous progress in this field. Owing to the complexity of the modern engineering system and some inevitable uncertainties in-cluding the modeling error, parameter time delay, uncertain parameters, unmodeled dynamics and disturbance, We fail to acquire the satisfied solution and many conclusions of modern con-trol theory can't work effectively in practical engineering application. So uncertain nonlinear system control research has been retaining a certain hot spot up to now.
Adaptive theory is a nonlinear control methodology, which is particularly useful for control of highly uncertain nonlinear system and complex systems.In recent years, with the develop-ment of the nonlinear backstepping adaptive technique and neural networks, in the design and analysis of uncertain nonlinear control system, the adaptive neural network control based back-stepping approach has become the highlight in the control theory, and become a new re-search direction in the neural network control field. Some correlative issues in this area are stud-ied in this paper. An adaptive neural network control scheme which employs the back-stepping technique based on Lyapunov stability theory and neural network control theory for a class of SISO uncertain nonlinear system is designed in this paper.
The thesis consists of the following five papers:
In chapter 1,introduce the background of the topic, the research situations and the research purpose and significance of the uncertain nonlinear adaptive control.
In chapter 2,introduce the basis theory involved in the paper,including the basis concepts, the main lemma and the important inequalities.Such as Lyapunov stability theory, the backstep-ping control theory and the inequalities used frequently in the paper.
In chapter 3,an adaptive neural networks control approach was developed for a class of SISO uncertain nonlinear systems using the back-stepping technique.,and realize the semi-global boundedness for all signals and at the same time, the tracking error is as small as possible.
In chapter 4, consider a class of nonlinear system with uncertain control directions, an adap-tive neural networks controller was proposed using the neural network approximation princi-ple,the Lyapunov stability theory and the back-stepping technique,and realize the semi-global boundedness for all signals and at the same time, the tracking error is as small as possible.
In chapter 5,we summarize the dissertation and discuss open problems for future research.
自适应理论作为一种不确定非线性控制策略,特别适用于控制复杂的不确定非线性系统.最近几年,随着非线性backstepping自适应技术和神经网络的发展,在不确定非线性控制系统的设计和分析中,基于backstepping方法的自适应神经网络控制问题,已引起人们的广泛关注,并成为神经网络控制领域中的一个新的研究方向.本文就此领域的相关问题展开研究.本人基于Lyapunov稳定性理论和backstepping方法以及神经网络控制理论,对一类单输入单输出不确定非线性的系统,提出了一种自适应神经网络backstepping控制方法.
论文共包括五部分内容：
第一章：介绍了所研究课题的背景知识,综述了非线性不确定系统自适应控制的研究现状和研究目的意义.
第二章：介绍论文所涉及的基础理论,包括基本概念、主要定理、引理和重要方法.如Lyapunov稳定性理论,backstepping设计方法等,以及几个论文中多次用到的不等式.
第三章：研究了一类单输入单输出不确定非线性系统,采用backstepping方法,设计了自适应神经网络控制器,实现了系统所有信号的有界以及跟踪误差的尽可能小.
第四章：研究了一类具有控制方向的不确定非线性系统的,利用神经网络逼近原理,backstepping控制方法及Lyapunov稳定性理论,设计了自适应神经网控制器,实现了系统所有信号的有界以及跟踪误差的尽可能小.
第五章：对全文进行了总结,并提出下一步研究的方向.
In the recent years, it has developed greatly in the control theory research and application of control design for nonlinear systems, and people have gained tremendous progress in this field. Owing to the complexity of the modern engineering system and some inevitable uncertainties in-cluding the modeling error, parameter time delay, uncertain parameters, unmodeled dynamics and disturbance, We fail to acquire the satisfied solution and many conclusions of modern con-trol theory can't work effectively in practical engineering application. So uncertain nonlinear system control research has been retaining a certain hot spot up to now.
Adaptive theory is a nonlinear control methodology, which is particularly useful for control of highly uncertain nonlinear system and complex systems.In recent years, with the develop-ment of the nonlinear backstepping adaptive technique and neural networks, in the design and analysis of uncertain nonlinear control system, the adaptive neural network control based back-stepping approach has become the highlight in the control theory, and become a new re-search direction in the neural network control field. Some correlative issues in this area are stud-ied in this paper. An adaptive neural network control scheme which employs the back-stepping technique based on Lyapunov stability theory and neural network control theory for a class of SISO uncertain nonlinear system is designed in this paper.
The thesis consists of the following five papers:
In chapter 1,introduce the background of the topic, the research situations and the research purpose and significance of the uncertain nonlinear adaptive control.
In chapter 2,introduce the basis theory involved in the paper,including the basis concepts, the main lemma and the important inequalities.Such as Lyapunov stability theory, the backstep-ping control theory and the inequalities used frequently in the paper.
In chapter 3,an adaptive neural networks control approach was developed for a class of SISO uncertain nonlinear systems using the back-stepping technique.,and realize the semi-global boundedness for all signals and at the same time, the tracking error is as small as possible.
In chapter 4, consider a class of nonlinear system with uncertain control directions, an adap-tive neural networks controller was proposed using the neural network approximation princi-ple,the Lyapunov stability theory and the back-stepping technique,and realize the semi-global boundedness for all signals and at the same time, the tracking error is as small as possible.
In chapter 5,we summarize the dissertation and discuss open problems for future research.
引文
[1]刘吉宾.交流伺服系统的神经网络自适应控制[D].南京理工大学硕士论文,2004.
[2]沈艳霞,林谨等.感应电机backstepping控制方法及dSPACE实时仿真研究[J].系统仿真学报,2005,17(9)：2207-2210.
[3]井元伟,李云磊等TCSC的非线性逆推设计[J].东北大学学报(自然科学报),2003.24(1)：4-6.
[4]王宝华,杨成梧等.发电机的非线性自适应逆推控制理论与应用[J],2006.23(1)：60-64.
[5]李文磊,张智焕等.基于自适应backstepping设计的TCSC的非线性鲁棒控制器[J].控制理论与应用,2005,22(1)：153-156.
[6]李文磊,井元伟等.非线性气门控制器的自适应鲁棒逆推设计[J].中国电机工程学报,2003,23(1)：155-158.
[7]Niu Yugang, Zou Yun,Yang Chengwu.Neural network-based adaptive tracking control for a class of nonlinear systems[J].Control Theory and Application of China,2001,18(3):461-464.
[8]Patino H D,Liu D.Neural network-based model reference adaptive control system[J].IEEE Trans Sys Man&Cybernetics,2000,30(1):198-204.
[9]Narendra K S,Parthasarathy K.Identification and control of dynamical systems using neural networks[J].IEEE Trans Neural Networks,1990,1(1):4-27.
[10]廖晓峰,李传东.神经网络研究的发展趋势[J].国际学术动态,2006,5：43-44
[11]刘兴堂.应用自适应控制[M].西安：西北工业大学出版社,2003.
[12]王树青等.先进控制技术及应用[M].北京：化学工业出版社,2001.
[13]R.M.Sanner and J.E.Slotine, Gaussian networks for direct adaptive control[J],IEEE Trans.Neural Networks,1992,vol.3,no.6 pp.837-863.
[14]F.C.Chen and H.K.Kalil, Adaptive control for a class of nonlinear discrete-time systems us-ingneural networks[J],IEEE Trans.Automat.Control,vol.40,no.5,pp.791-801,1995.
[15]T.Zhang,S.S.Ge and C.C.Hang, Adaptive neural network for strict-feedback stepping nonlinear systems using backstepping design,Automatica,Vol.36.,pp.1835-1846,2000.
[16]Kanellakopoulos,I.,Kokotovic,p.& Morse,A.Systematic design of adaptive controllers for feedback linearizable systems[J].IEEE Trans on Automat.Contr,36(11):1241-1253,1991.
[17]陈刚,一类不确定非线性系统的鲁棒自适应控制[J].系统工程理论与实践.2006,12：78-84.
[18]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,Suppl.
[19]赵文杰.不确定非线性系统的变结构控制[D].华北电力大学工学博士学位论文.2004.
[20]M.M.Polycarpou,Stable adaptive neural control scheme for nonlinear systems[J],IEEE Trans Automat.Control,1996,vol.41,no.3,pp.447-451.
[21]M.M.Polycarpou and M.J.Mears,stable adaptive tracking of uncertain systems using nonlinearly parametrized on-line approximators,International Journal of Con-trol,1998,vol.70,no.3,pp.363-384.
[22]Y.Zhang,S.S.Ge,and Z.P.Jiang, stable neural controller design for unknown nonlinearsys-tems using backstepping[J],IEEE Trans.Neural Networks,2000,vol.11, pp.1347-1359.
[23]邵克勇,高宏宇,于显利,杨圆圆,张会珍.不确定非线性系统神经网络自适应控制[J].控制工程,2007,14(1)：42-44.
[24]高宏宇.不确定系统的神经网络控制研究[D].大庆石油学院硕士学位论文,2006.
[25]朱永红.非线性不确定系统鲁棒自适应控制研究[D].浙江大学博士学位论文,2003.
[26]陈刚.不确定非线性系统鲁棒自适应控制研究[D].浙江大学博士学位论文,2006.
[27]王强德,井元伟,张嗣瀛,王忠锐,非线性参数化系统的鲁棒自适应输出跟踪控制.第23届中国控制会议论文集,pp.718-721,2004.
[28]谢克明.现代控制理论基础[M].北京：北京工业大学出版社,2003.497-500.
[29]廖晓昕.动力系统的稳定性理论和应用[M].北京：国防工业出版社,2000.56-57.
[30]Krstic M.,Deng H..Stabilization of Uncertain Systems[M].New York:Springer,1998.
[31]王冰.不确定广义下三角结构非线性系统的鲁棒自适应控制及其在电力系统中的应用 [D].合肥：中国科技大学,2006.
[32]M.Krstic,I.Kanellakopoulos,and P.Kokotovic,Nonlinear and adaptive control de-sign[M].New York:Wiley,1995.
[33]S S Ge,C Wang.Direct adaptive NN control of a class of nonlinear systems[J].IEEE Trans.Neural Networks,2002,13(1):214-221.
[34]S S Ge,C Wang.Adaptive neural control of uncertain MIMO nonlinear systems[J].IEEE Trans.Neural Networks,2004,15(3):674-692.
[35]Y H Li,S Qiang,X Y Zhuang,etal.Robust and Adaptive backstepping control for nonlinear systems using RBF neural networks[J].IEEE Trans.On Neural Networks,2004,15(3):693-701.
[36]S S Ge,F.Hong,H.L.Lee,"Adaptive neural control of nonlinear time-delay systems with un-known virtul control coefficients,"in IEEE Translations on System,Man,and Cybernet-ics,vol.1,2004,pp.499-516.
[2]沈艳霞,林谨等.感应电机backstepping控制方法及dSPACE实时仿真研究[J].系统仿真学报,2005,17(9)：2207-2210.
[3]井元伟,李云磊等TCSC的非线性逆推设计[J].东北大学学报(自然科学报),2003.24(1)：4-6.
[4]王宝华,杨成梧等.发电机的非线性自适应逆推控制理论与应用[J],2006.23(1)：60-64.
[5]李文磊,张智焕等.基于自适应backstepping设计的TCSC的非线性鲁棒控制器[J].控制理论与应用,2005,22(1)：153-156.
[6]李文磊,井元伟等.非线性气门控制器的自适应鲁棒逆推设计[J].中国电机工程学报,2003,23(1)：155-158.
[7]Niu Yugang, Zou Yun,Yang Chengwu.Neural network-based adaptive tracking control for a class of nonlinear systems[J].Control Theory and Application of China,2001,18(3):461-464.
[8]Patino H D,Liu D.Neural network-based model reference adaptive control system[J].IEEE Trans Sys Man&Cybernetics,2000,30(1):198-204.
[9]Narendra K S,Parthasarathy K.Identification and control of dynamical systems using neural networks[J].IEEE Trans Neural Networks,1990,1(1):4-27.
[10]廖晓峰,李传东.神经网络研究的发展趋势[J].国际学术动态,2006,5：43-44
[11]刘兴堂.应用自适应控制[M].西安：西北工业大学出版社,2003.
[12]王树青等.先进控制技术及应用[M].北京：化学工业出版社,2001.
[13]R.M.Sanner and J.E.Slotine, Gaussian networks for direct adaptive control[J],IEEE Trans.Neural Networks,1992,vol.3,no.6 pp.837-863.
[14]F.C.Chen and H.K.Kalil, Adaptive control for a class of nonlinear discrete-time systems us-ingneural networks[J],IEEE Trans.Automat.Control,vol.40,no.5,pp.791-801,1995.
[15]T.Zhang,S.S.Ge and C.C.Hang, Adaptive neural network for strict-feedback stepping nonlinear systems using backstepping design,Automatica,Vol.36.,pp.1835-1846,2000.
[16]Kanellakopoulos,I.,Kokotovic,p.& Morse,A.Systematic design of adaptive controllers for feedback linearizable systems[J].IEEE Trans on Automat.Contr,36(11):1241-1253,1991.
[17]陈刚,一类不确定非线性系统的鲁棒自适应控制[J].系统工程理论与实践.2006,12：78-84.
[18]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,Suppl.
[19]赵文杰.不确定非线性系统的变结构控制[D].华北电力大学工学博士学位论文.2004.
[20]M.M.Polycarpou,Stable adaptive neural control scheme for nonlinear systems[J],IEEE Trans Automat.Control,1996,vol.41,no.3,pp.447-451.
[21]M.M.Polycarpou and M.J.Mears,stable adaptive tracking of uncertain systems using nonlinearly parametrized on-line approximators,International Journal of Con-trol,1998,vol.70,no.3,pp.363-384.
[22]Y.Zhang,S.S.Ge,and Z.P.Jiang, stable neural controller design for unknown nonlinearsys-tems using backstepping[J],IEEE Trans.Neural Networks,2000,vol.11, pp.1347-1359.
[23]邵克勇,高宏宇,于显利,杨圆圆,张会珍.不确定非线性系统神经网络自适应控制[J].控制工程,2007,14(1)：42-44.
[24]高宏宇.不确定系统的神经网络控制研究[D].大庆石油学院硕士学位论文,2006.
[25]朱永红.非线性不确定系统鲁棒自适应控制研究[D].浙江大学博士学位论文,2003.
[26]陈刚.不确定非线性系统鲁棒自适应控制研究[D].浙江大学博士学位论文,2006.
[27]王强德,井元伟,张嗣瀛,王忠锐,非线性参数化系统的鲁棒自适应输出跟踪控制.第23届中国控制会议论文集,pp.718-721,2004.
[28]谢克明.现代控制理论基础[M].北京：北京工业大学出版社,2003.497-500.
[29]廖晓昕.动力系统的稳定性理论和应用[M].北京：国防工业出版社,2000.56-57.
[30]Krstic M.,Deng H..Stabilization of Uncertain Systems[M].New York:Springer,1998.
[31]王冰.不确定广义下三角结构非线性系统的鲁棒自适应控制及其在电力系统中的应用 [D].合肥：中国科技大学,2006.
[32]M.Krstic,I.Kanellakopoulos,and P.Kokotovic,Nonlinear and adaptive control de-sign[M].New York:Wiley,1995.
[33]S S Ge,C Wang.Direct adaptive NN control of a class of nonlinear systems[J].IEEE Trans.Neural Networks,2002,13(1):214-221.
[34]S S Ge,C Wang.Adaptive neural control of uncertain MIMO nonlinear systems[J].IEEE Trans.Neural Networks,2004,15(3):674-692.
[35]Y H Li,S Qiang,X Y Zhuang,etal.Robust and Adaptive backstepping control for nonlinear systems using RBF neural networks[J].IEEE Trans.On Neural Networks,2004,15(3):693-701.
[36]S S Ge,F.Hong,H.L.Lee,"Adaptive neural control of nonlinear time-delay systems with un-known virtul control coefficients,"in IEEE Translations on System,Man,and Cybernet-ics,vol.1,2004,pp.499-516.