基于模糊/神经网络的非线性MIMO自适应反推控制
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摘要
本文研究提出了一种基于模糊／神经网络控制的多输入多输出(MIMO)自适应反推控制方法。考虑以下更广类型的MIMO非线性系统：
其中为系统的状态，u_j∈R,y_j∈R分别为系统的输入和输出。。f_(i,j)(·)，g_(i,j)(·)，f_(i,p_i)(·)，β_(i,j)(·)都为未知的非线性光滑函数，并假定β_(i,j)(x)＞0，i=1，2，……，m，j=1，2，……，p_i-1。
本文主要贡献有三点：
第一：系统的复杂性：系统(1)是由具有相互耦合的子系统组成。相对于文献[6]，系统出现了未知非线性函数；相对于文献[39]，系统的耦合性上更具一般性。
第二：结果的优越性：我们将利用系统中仿射项特殊形式，建立一种自适应模糊／神经网络控制方法，完全避免控制器的奇异性问题。在控制设计中，利用模糊／神经网络来逼近未知非线性函数，能保证闭环系统所有信号和参数误差有界，并且跟踪误差渐近收敛到零。而一般的自适应反推控制大只是保证跟踪误差全局一致有界。
第三：设计的灵活性：基于不同的系统条件，我们给出了两种不同的控制方法。可根据具体系统灵活选取控制策略。
全文的组织结构如下：
第一章是绪论，首先简要叙述非线性自适应控制技术的主要研究内容及
其研究现状;着重分析自适应反推设计法(baoks tePping);指出现有非线性
自适应控制技术存在的问题;最后提出本文的研究目标和内容.
第二章提出了一种针对模糊神经网络的可变步长学习算法.针对现行
模糊神经网络的收敛速度慢，稳定性难以保证的问题，提出了一种可
变步长的学习方法，找到了一个使网络既能保证收敛又具有较快速度
的有效选!择方案.
第三章首先给出了一种具有相互藕合性的复杂非线性多输入多输出系
统，它包含了许多常见的非线性系统类型;基于模糊/神经网络控制技术，
提出了一种自适应反推控制新方法.该方法不仅能保证闭环系统所有信号和
参数误差有界，更能使得跟踪误差渐近收敛到零，这优于一般自适应反推算
法中的全局一致性结果.
作者在第四章对全文进行了总结，阐明了本文研究的特点，指出T目前
工作中尚存在的不足与问题，并对今后的研究工作进行了展望.
In this thesis, adaptive fuzzy/neural control schemes are presented for a class of uncertain MIMO nonlinear systems. We consider the follow broader class of multi-input/multi-output (MIMO) nonlinear systems.
Where are the states of the system, and are the system inputs and outputs, respectively;
are unknown nonlinear smooth functions.
The main special features or this thesis are as follows:
(i) The complex of the system: The MIMO system is composed of subsystems which are interconnected. Compared with the MIMO system consided in [39], the MIMO system in this thesis is more general in system state interconnections, which makes it difficult to control the systems.
(ii) The better result of the control: By exploiting the special properties of the affine terms of the MIMO system, the developed scheme avoids the controller singularity problem completely without using projection algorithms. By employing NNs to approximate all the uncertain nonlinear functions in the controller design, the developed scheme achieves boundedness of all the signals in the closed-loop of the MIMO systems. The tracking error converges to zero
asymptotically. In most of the backstepping design methodology, all the solutions are globally uniformly bounded.
(Hi) The flexibility of design: as show in this thesis, the control design is not unique. In actual applications, different types of control maybe used for the best result.
The thesis is brganized as follows:
Chapter 1 introduces the basic concepts and methods of nonlinear adaptive control technology, especially on adaptive backsepping design. The chapter ends with the depiction of the primary research objectives of the thesis.
In chapter 2, In order to avoid the difficulties of poor convergent and instability in neural control design, we propose a variational learning-rate in the neural network learning algorithm, the stability and convergence with faster speed can be guaranteed.
In chapter 3, we consider adaptive neural control of the broader class of multi-input/multi-output (MIMO) nonlinear systems, which is composed of subsystems which are interconnected. Based on the universal approximation capability of fuzzy/neural networks, we design a novel adaptive backstepping method to achieve not only boundedness of all the signals in the closed-loop of the MIMO systems but also the tracking error converges to zero asymptotically.
The final chapter summarizes the main results and makes conclusions of the dissertation. Some future research work is also described.
其中为系统的状态，u_j∈R,y_j∈R分别为系统的输入和输出。。f_(i,j)(·)，g_(i,j)(·)，f_(i,p_i)(·)，β_(i,j)(·)都为未知的非线性光滑函数，并假定β_(i,j)(x)＞0，i=1，2，……，m，j=1，2，……，p_i-1。
本文主要贡献有三点：
第一：系统的复杂性：系统(1)是由具有相互耦合的子系统组成。相对于文献[6]，系统出现了未知非线性函数；相对于文献[39]，系统的耦合性上更具一般性。
第二：结果的优越性：我们将利用系统中仿射项特殊形式，建立一种自适应模糊／神经网络控制方法，完全避免控制器的奇异性问题。在控制设计中，利用模糊／神经网络来逼近未知非线性函数，能保证闭环系统所有信号和参数误差有界，并且跟踪误差渐近收敛到零。而一般的自适应反推控制大只是保证跟踪误差全局一致有界。
第三：设计的灵活性：基于不同的系统条件，我们给出了两种不同的控制方法。可根据具体系统灵活选取控制策略。
全文的组织结构如下：
第一章是绪论，首先简要叙述非线性自适应控制技术的主要研究内容及
其研究现状;着重分析自适应反推设计法(baoks tePping);指出现有非线性
自适应控制技术存在的问题;最后提出本文的研究目标和内容.
第二章提出了一种针对模糊神经网络的可变步长学习算法.针对现行
模糊神经网络的收敛速度慢，稳定性难以保证的问题，提出了一种可
变步长的学习方法，找到了一个使网络既能保证收敛又具有较快速度
的有效选!择方案.
第三章首先给出了一种具有相互藕合性的复杂非线性多输入多输出系
统，它包含了许多常见的非线性系统类型;基于模糊/神经网络控制技术，
提出了一种自适应反推控制新方法.该方法不仅能保证闭环系统所有信号和
参数误差有界，更能使得跟踪误差渐近收敛到零，这优于一般自适应反推算
法中的全局一致性结果.
作者在第四章对全文进行了总结，阐明了本文研究的特点，指出T目前
工作中尚存在的不足与问题，并对今后的研究工作进行了展望.
In this thesis, adaptive fuzzy/neural control schemes are presented for a class of uncertain MIMO nonlinear systems. We consider the follow broader class of multi-input/multi-output (MIMO) nonlinear systems.
Where are the states of the system, and are the system inputs and outputs, respectively;
are unknown nonlinear smooth functions.
The main special features or this thesis are as follows:
(i) The complex of the system: The MIMO system is composed of subsystems which are interconnected. Compared with the MIMO system consided in [39], the MIMO system in this thesis is more general in system state interconnections, which makes it difficult to control the systems.
(ii) The better result of the control: By exploiting the special properties of the affine terms of the MIMO system, the developed scheme avoids the controller singularity problem completely without using projection algorithms. By employing NNs to approximate all the uncertain nonlinear functions in the controller design, the developed scheme achieves boundedness of all the signals in the closed-loop of the MIMO systems. The tracking error converges to zero
asymptotically. In most of the backstepping design methodology, all the solutions are globally uniformly bounded.
(Hi) The flexibility of design: as show in this thesis, the control design is not unique. In actual applications, different types of control maybe used for the best result.
The thesis is brganized as follows:
Chapter 1 introduces the basic concepts and methods of nonlinear adaptive control technology, especially on adaptive backsepping design. The chapter ends with the depiction of the primary research objectives of the thesis.
In chapter 2, In order to avoid the difficulties of poor convergent and instability in neural control design, we propose a variational learning-rate in the neural network learning algorithm, the stability and convergence with faster speed can be guaranteed.
In chapter 3, we consider adaptive neural control of the broader class of multi-input/multi-output (MIMO) nonlinear systems, which is composed of subsystems which are interconnected. Based on the universal approximation capability of fuzzy/neural networks, we design a novel adaptive backstepping method to achieve not only boundedness of all the signals in the closed-loop of the MIMO systems but also the tracking error converges to zero asymptotically.
The final chapter summarizes the main results and makes conclusions of the dissertation. Some future research work is also described.
引文
[1] 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
[2] IsidoriA. Nonlinear Control Systems. ThirdEdition, NewYork, Spinger-Verleg, 1995
[3] 高为炳 非线性控制系统导论[M]．北京：中国科学出版社 1988
[4] 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．控制与决策Vol.17Suppl．Nov．2002
[5] 夏小华，高为炳．非线性系统控制及解耦[M]．北京：科学出版社，1997
[6] Krstic M, Kanellakopoulos I, Kokotovic P V. Nonlinear and Adaptive Control Design, NewYork: Wiley, 1995
[7] P.A.Ioannou and J.Sun. Robust Adaptive Control. Englewood Cliffs,NJ:Prentice-Hall, 1995
[8] Lam H K, Leung F H F, Tam P K S. Stable and robust fuzzy control for uncertain nonlinear systems[J].IEEE Trans. On Sytems, Man Cybernetics, 2000, 30-A(6):825～840
[9] Tong Shao-cheng, etc. Fuzzy adaptive control of multivariable nonlinear systems[J].Fuzzy Sets and Systems, 2000, 111:163～167
[10] Hsu Feng-yi, Fu Li-chen. A novel adaptive fuzzy variable structure control for a class of nonlinear uncertain systems via backsepping [J]. Fuzzy Sets and System, 2001, 122(1):83～106
[11] 张乃尧 阎平凡．神经网络与模糊控制．北京：清华大学出版社 1998
[12] S.S.Ge C.C.Hang et al. Stable adaptive neural network control. KLURWER ACADEMIC PUBLISHERS Boston Dordrecht London, 2002
[13] KanellakopoulosI, P Kokotovic, A S Morse. Syste-matic design of
adaptive controllers for feedback linearizable systems[J].IEEE Trans on AC, 1991, 36(11):1241～1253
[14] 周绍生，费树岷，冯纯伯．不确定严格反馈非线性系统的鲁棒控制[J]．信息与控制，2000，29(3)：193～197
[15] 胡云安，吴广彬，郭晓军．一类非线性系统的多面滑模控制[J]．控制与决策，2000，15(4)：497～500
[16] 余星火，武玉强．不确定非线性系统的自适应最终滑模控制--Backs tepping方法[J]．控制理论与应用，1998，15(6)：900～907
[17] 陈卫田，周绍生，颜世田，初学导．一类不确定非线性系统的鲁棒输出反馈控制[J]．控制理论与应用，1998，15(5)：668～674
[18] 王强德，魏春玲，陈卫田．不确定非线性系统的鲁棒输出反馈自适应控制[J]．控制与决策，1999，14(6)：688～693
[19] 陈卫田，施颂椒，张钟俊．一类不确定非线性系统的适应输出反馈控制[J]．数学物理学报，1998，18(2)：140～148
[20] Ying Zhang, etc. Robust decentralized adaptive stabilization of interconnected systems with guaranteed transient performance [J]. Automatica, 2000,36(6):907～915
[21] T Zhang, S S Ge, C C Hang. Adaptive neural network control for strict-feedback nonlinear systems using backstepping design[J]. Automatica, 2000,36(12): 1835～1846
[22] 李琳琳，赵光恒，赵长安．不确定非线性系统鲁棒控制研究．宇航学报，2003，Vo 1．24，No．4
[23] 程代展，洪奕光，秦化淑．多输入非线性系统后推(backstepping)型[J]．控制理论与应用，1998，15(6)：824～830
[24] 宫琪，田玉平．非线性交叉严格反馈系统的一种构造型设计方法[J]．自动化学报，2000，26(4)：447～453
[25] 王立新．自适应模糊系统与控制—设计与稳定性分析．北京：国防工业出版社，1995
[26] S. Haykin, Neural networks-a comprehensive approach, Macmillan
Publishing Company, 1994
[27] N. Y. K. Hornik, etc. Multilayer feedforward networks are universal approximators, Neural Networks, 1989, vol. 2, pp. 359～366
[28] 汤跃忠，张乃尧，李衍达 模糊神经网络及其在智能控制中的应用：清华大学学报，1995，35(增3)82～88
[29] Chen.Y.C,Teng.C.C A model reference control structure using a fuzzy neural network. Fuzzy Sets and Systems. 1995 73:291～312
[30] C.C.Ku and K.Y..Lee. Diagonal recurrent neural network for dynamic systems control. IEEE. Trans. Neural Networks. 1995
[31] Scarselli F, Tsoi A H. Universal approximation using feedforward neural networks:A survey of some existing methods,and some new results[J].Neural Networks, 1998,11 (1): 15～37
[32] Choi J Y, etc. Adaptive observer backstepping control using neural networks[J].IEEE Trans.Neural Networks, 2001,12(5): 1103～1112
[33] Knohl T, Unbehauen H. ANNNAC-extension of adaptive backstepping algorthm with artificial neural networlks[J].IEEE Proc-control theory appl, 2000,147(2):177～183
[34] Zhan f Y, Peng P Y, Jiang Z R Stable neural controller design for unknown nonlinear systems using backstepping[J]. IEEE Trans. Neural networks, 2000, 11(6):1347～1360
[35] Hyeongcheol L and Masayoshi T. Robust Adaptive Control Using a Universal Approxoimator for SISO Nonlinear Systems. IEEE Trans. On Fuzzy Systems, 2000.8(1):95～106
[36] Jin Y C, Jay A. Adaptive Observer Backstepping Control Using Neural Network. IEEE Trans.On Neural Networks. 2001, 12(5): 1103～1112
[37] R. Ordonez and K. M. Passino. Stable Multi-Input Multi-Output Adaptive Fuzzy/Neural Control. IEEE Trans. On Fuzzy Systems, 1999, 7(3): 345～353
[38] F.C.Chen and H.K.Khalil. Adaptive control of a class of nonlear
discrete-time systems using neral networks.IEEE Trans. Automatic Control, 1995,40:791～801
[39] S.S.Ge,C.C.Hang,and T.Zhang. Stable adaptive control for nonlinear multivariable systems with a triangular control structure. IEEE Trans. On Automatic Control, 2000, 45:1221～1225
[40] 佟绍成，柴天佑．一类多变量非线性动态系统的鲁棒自适应模糊控制[J]．自动化学报，2000，26(5)：630～635
[41] 王涛．一类非线性系统的间接自适应输出反馈控制[J]．控制与决策，2000，15(2)：161～164
[42] 佟绍成，周军．非线性模糊间接和直接自适应控制器的设计和稳定性分析[J]．控制与决策，2000，15(3)：293～296
[43] 刘国荣，万百五．一类非线性MIMO系统的间接自适应模糊鲁棒控制．控制与决策，2002，17 Supp1：676～680
[44] 刘国荣，万百五．一类非线性MIMO系统的直接自适应模糊鲁棒控制．控制理论与应用，2002，19(5)：693～698
[45] 朴营国，何希勤，张化光．一种多输入多输出模糊自适应控制方法的研究．自动化学报，2000，26(1)：105～110
[46] 张天平．一类MIMO非线性系统的稳定自适应模糊控制．模糊与数学，2002，16(4)：94～99
[47] Zhang T, Ge S S,Hang C C. Stable adaptive control for a class of nonlinear systems using a modified Lyapunov fanction[J].IEEE Trans. On Automatic Control, 2000, 45(1): 129～132
[48] M.M.Polycarpou and EA.Ioannou. A robust adaptive nonlinear control design. Automatica, 1996, 32:423～427
[49] B.Yao and M.Tomizuka. Adaptive robust control of siso nonlinear systems in a semi-strict feedback form. Automatica, 1997, 33:893～900
[2] IsidoriA. Nonlinear Control Systems. ThirdEdition, NewYork, Spinger-Verleg, 1995
[3] 高为炳 非线性控制系统导论[M]．北京：中国科学出版社 1988
[4] 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．控制与决策Vol.17Suppl．Nov．2002
[5] 夏小华，高为炳．非线性系统控制及解耦[M]．北京：科学出版社，1997
[6] Krstic M, Kanellakopoulos I, Kokotovic P V. Nonlinear and Adaptive Control Design, NewYork: Wiley, 1995
[7] P.A.Ioannou and J.Sun. Robust Adaptive Control. Englewood Cliffs,NJ:Prentice-Hall, 1995
[8] Lam H K, Leung F H F, Tam P K S. Stable and robust fuzzy control for uncertain nonlinear systems[J].IEEE Trans. On Sytems, Man Cybernetics, 2000, 30-A(6):825～840
[9] Tong Shao-cheng, etc. Fuzzy adaptive control of multivariable nonlinear systems[J].Fuzzy Sets and Systems, 2000, 111:163～167
[10] Hsu Feng-yi, Fu Li-chen. A novel adaptive fuzzy variable structure control for a class of nonlinear uncertain systems via backsepping [J]. Fuzzy Sets and System, 2001, 122(1):83～106
[11] 张乃尧 阎平凡．神经网络与模糊控制．北京：清华大学出版社 1998
[12] S.S.Ge C.C.Hang et al. Stable adaptive neural network control. KLURWER ACADEMIC PUBLISHERS Boston Dordrecht London, 2002
[13] KanellakopoulosI, P Kokotovic, A S Morse. Syste-matic design of
adaptive controllers for feedback linearizable systems[J].IEEE Trans on AC, 1991, 36(11):1241～1253
[14] 周绍生，费树岷，冯纯伯．不确定严格反馈非线性系统的鲁棒控制[J]．信息与控制，2000，29(3)：193～197
[15] 胡云安，吴广彬，郭晓军．一类非线性系统的多面滑模控制[J]．控制与决策，2000，15(4)：497～500
[16] 余星火，武玉强．不确定非线性系统的自适应最终滑模控制--Backs tepping方法[J]．控制理论与应用，1998，15(6)：900～907
[17] 陈卫田，周绍生，颜世田，初学导．一类不确定非线性系统的鲁棒输出反馈控制[J]．控制理论与应用，1998，15(5)：668～674
[18] 王强德，魏春玲，陈卫田．不确定非线性系统的鲁棒输出反馈自适应控制[J]．控制与决策，1999，14(6)：688～693
[19] 陈卫田，施颂椒，张钟俊．一类不确定非线性系统的适应输出反馈控制[J]．数学物理学报，1998，18(2)：140～148
[20] Ying Zhang, etc. Robust decentralized adaptive stabilization of interconnected systems with guaranteed transient performance [J]. Automatica, 2000,36(6):907～915
[21] T Zhang, S S Ge, C C Hang. Adaptive neural network control for strict-feedback nonlinear systems using backstepping design[J]. Automatica, 2000,36(12): 1835～1846
[22] 李琳琳，赵光恒，赵长安．不确定非线性系统鲁棒控制研究．宇航学报，2003，Vo 1．24，No．4
[23] 程代展，洪奕光，秦化淑．多输入非线性系统后推(backstepping)型[J]．控制理论与应用，1998，15(6)：824～830
[24] 宫琪，田玉平．非线性交叉严格反馈系统的一种构造型设计方法[J]．自动化学报，2000，26(4)：447～453
[25] 王立新．自适应模糊系统与控制—设计与稳定性分析．北京：国防工业出版社，1995
[26] S. Haykin, Neural networks-a comprehensive approach, Macmillan
Publishing Company, 1994
[27] N. Y. K. Hornik, etc. Multilayer feedforward networks are universal approximators, Neural Networks, 1989, vol. 2, pp. 359～366
[28] 汤跃忠，张乃尧，李衍达 模糊神经网络及其在智能控制中的应用：清华大学学报，1995，35(增3)82～88
[29] Chen.Y.C,Teng.C.C A model reference control structure using a fuzzy neural network. Fuzzy Sets and Systems. 1995 73:291～312
[30] C.C.Ku and K.Y..Lee. Diagonal recurrent neural network for dynamic systems control. IEEE. Trans. Neural Networks. 1995
[31] Scarselli F, Tsoi A H. Universal approximation using feedforward neural networks:A survey of some existing methods,and some new results[J].Neural Networks, 1998,11 (1): 15～37
[32] Choi J Y, etc. Adaptive observer backstepping control using neural networks[J].IEEE Trans.Neural Networks, 2001,12(5): 1103～1112
[33] Knohl T, Unbehauen H. ANNNAC-extension of adaptive backstepping algorthm with artificial neural networlks[J].IEEE Proc-control theory appl, 2000,147(2):177～183
[34] Zhan f Y, Peng P Y, Jiang Z R Stable neural controller design for unknown nonlinear systems using backstepping[J]. IEEE Trans. Neural networks, 2000, 11(6):1347～1360
[35] Hyeongcheol L and Masayoshi T. Robust Adaptive Control Using a Universal Approxoimator for SISO Nonlinear Systems. IEEE Trans. On Fuzzy Systems, 2000.8(1):95～106
[36] Jin Y C, Jay A. Adaptive Observer Backstepping Control Using Neural Network. IEEE Trans.On Neural Networks. 2001, 12(5): 1103～1112
[37] R. Ordonez and K. M. Passino. Stable Multi-Input Multi-Output Adaptive Fuzzy/Neural Control. IEEE Trans. On Fuzzy Systems, 1999, 7(3): 345～353
[38] F.C.Chen and H.K.Khalil. Adaptive control of a class of nonlear
discrete-time systems using neral networks.IEEE Trans. Automatic Control, 1995,40:791～801
[39] S.S.Ge,C.C.Hang,and T.Zhang. Stable adaptive control for nonlinear multivariable systems with a triangular control structure. IEEE Trans. On Automatic Control, 2000, 45:1221～1225
[40] 佟绍成，柴天佑．一类多变量非线性动态系统的鲁棒自适应模糊控制[J]．自动化学报，2000，26(5)：630～635
[41] 王涛．一类非线性系统的间接自适应输出反馈控制[J]．控制与决策，2000，15(2)：161～164
[42] 佟绍成，周军．非线性模糊间接和直接自适应控制器的设计和稳定性分析[J]．控制与决策，2000，15(3)：293～296
[43] 刘国荣，万百五．一类非线性MIMO系统的间接自适应模糊鲁棒控制．控制与决策，2002，17 Supp1：676～680
[44] 刘国荣，万百五．一类非线性MIMO系统的直接自适应模糊鲁棒控制．控制理论与应用，2002，19(5)：693～698
[45] 朴营国，何希勤，张化光．一种多输入多输出模糊自适应控制方法的研究．自动化学报，2000，26(1)：105～110
[46] 张天平．一类MIMO非线性系统的稳定自适应模糊控制．模糊与数学，2002，16(4)：94～99
[47] Zhang T, Ge S S,Hang C C. Stable adaptive control for a class of nonlinear systems using a modified Lyapunov fanction[J].IEEE Trans. On Automatic Control, 2000, 45(1): 129～132
[48] M.M.Polycarpou and EA.Ioannou. A robust adaptive nonlinear control design. Automatica, 1996, 32:423～427
[49] B.Yao and M.Tomizuka. Adaptive robust control of siso nonlinear systems in a semi-strict feedback form. Automatica, 1997, 33:893～900
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