模糊神经网络控制器的优化设计
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摘要
模糊神经网络是将人工神经网络与模糊逻辑系统相结合的一种能处理抽象信息的网络，具有强大的自学习和自整定功能，是智能控制理论研究领域中一个十分活跃的分支，因此模糊神经网络控制的研究具有重要的意义。本文在分析模糊神经网络理论和应用现状的基础上，针对模糊神经网络控制中存在的一些问题，主要进行以下两个方面的研究：
1．针对模糊神经网络控制器一般存在着在线权值调整计算量大、训练时间长、过度修正权值可能导致系统剧烈振荡等缺点，提出了两种模糊神经网络控制器的优化方法：在线自学习过程中仅对控制性能影响大的控制规则相关的权值进行修正，以减小计算量，加快训练速度；基于T-S模糊模型，根据偏差及偏差变化率大小动态自适应调节权值修正步长，抑制控制器输出的剧烈变化，避免系统发生剧烈振荡。仿真结果表明本文提出的优化方法能大大减少在线权值修正的计算量，加快了系统的收敛速度。
2．由于传统控制器本身的局限，它们在非线性控制系统的设计和应用中存在许多问题，本文将模糊神经网络和传统控制策略相结合，设计了两种模糊神经网络自适应控制器：基于模糊基函数网络的间接型稳定自适应控制器和基于T-S模糊神经网络直接型稳定自适应控制器。首先用模糊神经网络
西安理工大学硕士学位论文
完成对控制系统未知结构或参数的逼近，然后根据Lyapunov稳定性定理设
计网络参数的自适应学习律，在线完成网络参数的调整，使系统满足
lyapunov稳定性。仿真结果表明，这两种控制器都能很好地实现跟踪输入
信号，并满足系统稳定性的要求。
Fuzzy neural network (FNN) is an active branch in the intelligent control. It is composed of the neural network and fuzzy logic system organically. And it is good at self-learning and self-tuning. So the theory of FNN is very important for the intelligent control. But there are still some problems in it. In this dissertation, the following theories and application of FNN are discussed.
1. The large account of compute work of updating weights and long training time usually discourage the FNN' s on-line application in industry. Moreover, when it is trained on-line to adapt to plant variations, the over-tuned may cause system oscillate extensively. In this dissertation, two kinds of optimization, methods are proposed. Firstly, only these linking weights corresponding to the control rules that affect the control performance significantly are updated in order to reduce the compute works and speed up the training progress. Secondly, the updating step is adjusted adaptively in accordance with the error and the change of error of the system based on the T-S model to get better performance. Simulation results show that the training time is reduced greatly and the convergence velocity is speed up.
2. It is difficult to design a traditional controller for some nonlinear
systems, as some parts of the system are unknown. In this dissertation, the FNN and the traditional controller are combined to design two kinds of FNN adaptive controllers for a class of nonlinear plant. They are stable indirect adaptive controller based on fuzzy basic function network and stable direct adaptive controller based on T-S fuzzy neural network. The FNN in the system is used to approximate the unknown parts of the system. Then according to the Lyapunov's stability theory, the adaptive laws of parameters are designed. The parameters of network are adjusted on line and the system satisfies the Lyapunov's stability. The simulation results show that these two kinds of adaptive controllers can realize tracing the input signal commendably and satisfy the request of stability simultaneously.
1．针对模糊神经网络控制器一般存在着在线权值调整计算量大、训练时间长、过度修正权值可能导致系统剧烈振荡等缺点，提出了两种模糊神经网络控制器的优化方法：在线自学习过程中仅对控制性能影响大的控制规则相关的权值进行修正，以减小计算量，加快训练速度；基于T-S模糊模型，根据偏差及偏差变化率大小动态自适应调节权值修正步长，抑制控制器输出的剧烈变化，避免系统发生剧烈振荡。仿真结果表明本文提出的优化方法能大大减少在线权值修正的计算量，加快了系统的收敛速度。
2．由于传统控制器本身的局限，它们在非线性控制系统的设计和应用中存在许多问题，本文将模糊神经网络和传统控制策略相结合，设计了两种模糊神经网络自适应控制器：基于模糊基函数网络的间接型稳定自适应控制器和基于T-S模糊神经网络直接型稳定自适应控制器。首先用模糊神经网络
西安理工大学硕士学位论文
完成对控制系统未知结构或参数的逼近，然后根据Lyapunov稳定性定理设
计网络参数的自适应学习律，在线完成网络参数的调整，使系统满足
lyapunov稳定性。仿真结果表明，这两种控制器都能很好地实现跟踪输入
信号，并满足系统稳定性的要求。
Fuzzy neural network (FNN) is an active branch in the intelligent control. It is composed of the neural network and fuzzy logic system organically. And it is good at self-learning and self-tuning. So the theory of FNN is very important for the intelligent control. But there are still some problems in it. In this dissertation, the following theories and application of FNN are discussed.
1. The large account of compute work of updating weights and long training time usually discourage the FNN' s on-line application in industry. Moreover, when it is trained on-line to adapt to plant variations, the over-tuned may cause system oscillate extensively. In this dissertation, two kinds of optimization, methods are proposed. Firstly, only these linking weights corresponding to the control rules that affect the control performance significantly are updated in order to reduce the compute works and speed up the training progress. Secondly, the updating step is adjusted adaptively in accordance with the error and the change of error of the system based on the T-S model to get better performance. Simulation results show that the training time is reduced greatly and the convergence velocity is speed up.
2. It is difficult to design a traditional controller for some nonlinear
systems, as some parts of the system are unknown. In this dissertation, the FNN and the traditional controller are combined to design two kinds of FNN adaptive controllers for a class of nonlinear plant. They are stable indirect adaptive controller based on fuzzy basic function network and stable direct adaptive controller based on T-S fuzzy neural network. The FNN in the system is used to approximate the unknown parts of the system. Then according to the Lyapunov's stability theory, the adaptive laws of parameters are designed. The parameters of network are adjusted on line and the system satisfies the Lyapunov's stability. The simulation results show that these two kinds of adaptive controllers can realize tracing the input signal commendably and satisfy the request of stability simultaneously.
引文
【1】顾树生等．自动控制原理[M]。北京：冶金工业出版社，2001：24—56．
【2】王立新。自适应模糊系统与控制—设计与稳定性分析[M]．北京国防工业出版社．
【3】Jin Ⅰ. Et al. Adaptive tracking of SISO nonlinear systems using multi-layered neural networks [J], IEEE Trans. on Neural Networks, 1(1), 1990: 4-27.
【4】Zadeh L. A. Fuzzy Set [M]. Information and Control, 8(3), 1965: 338-358.
【5】张化光．复杂系统的模糊辨识与模糊自适应控制[M]．沈阳：东北大学出版社，1993．
【6】Procyk T. J., Mamdani E. H. A linguistic self-organizing processes controller [J]. Automatica, 15(1), 1979: 15-30.
【7】Chung B. M., Oh J. H. Auto-tuning method of membership function in a fuzzy learning controller [J], journal of Intelligent and Fuzzy Systems, 1(4), 1994: 335-349.
【8】Wang L. X., Stable adaptive fuzzy control of nonlinear Systems [J], IEEE Trans. Fuzzy Syst. 1(2), 1993: t46-155.
【9】Zhang Y. Q, Kandel A. Compensatory neurofuzzy systems with fast learning algorithms [j]. IEEE Trans. on Neural Networks, 9(1), 1998: 83-105.
【10】Zhang J, Morris A. J. Recurrent Neuro-Fuzzy Networks for Nonlinear Process Modeling, IEEE Trans. on Neural Networks, 10(2), 1999: 313-326.
【11】Lee K M, Lwak D H, Kwang H L. Fuzzy Inference Neural Network for Fuzzy Model Tuning, IEEE Trans. on Systems, Man, and Cybernetics-Part B: Cybernetics, 26(4), 1996: 637-645.
【12】鲍鸿，黄心汉，李锡雄．广义模糊推理与广义模糊RBF神经网络[J]，控制与决策，15 (2)，2000：205-208．
【13】张昊，吴捷，郁滨．应用模糊神经网络进行负荷预测的研究[J]，自动化学报，25 (1)，1999：60-67．
【14】孙增圻，张再兴，邓志东．智能控制理论与技术[M]．北京：清华大学出版社，1997：170-180．
【15】Jang S R. ANFIS: Adaptive-network-based fuzzy inference system [J], IEEE Trans. on Systems, Man& Cybernetics, 23(3), 1993: 665-685.
【16】Wang L X, Mendel J M. Fuzzy basis functions, universal approximation and orthogonal least squares learning [J], IEEE Trans. on Neural Networks, 3(5), 1992: 807-814.
【17】李绍远等．智能控制的新进展[J]．控制与决策，15(1)，2000：1-5．
【18】Broomhead D S, Lowe D. Multivariable functional Interpolation and adaptive networks [J], Complex System, 2(4), 1988: 321-355.
【19】阎平凡，张常水．人工神经网络与模拟进化计算 [M]，清华大学出版社，2000．
【20】李人厚．智能控制理论和方法 [M]，西安电子科技大学出版社，1999．
【21】张立明．人工神经网络的模型及其应用 [M]，北京航空航天大学出版社，1993．
【22】陈燕庆．人工神经元网络在控制工程中的应用 [M]，西北工业大学出版社，1991．
【23】Chao C T, Chen Y J, Teng C C. Simplification of Fuzzy-Neural
System Using Similarity Analysis [J]. IEEE Trans. on Systems, Man and Cybernetics-Part B: Cybernetics, 26(3), 1996: 344-354,
【24】周志坚，毛宗源．一种最优模糊神经网络控制器 [J]．控制与决策，15(3)，2000：358—361．
【25】王震雷，顾树生，基于实值遗传算法的模糊神经网络辨识器，东北大学学报(自然科学版)，21 (4)，2000：354-356．
【26】Cao S G, Rees N W. Analysis and design for a class of complex control systems Part Ⅰ: Fuzzy modeling and identification [J]. Automatica, 33(11), 1997: 1017-1028.
【27】Takagi T, Sugeno M. A robust stabilization problem of fuzzy control systems and its application to backing up control of truck-trailer [J]. IEEE Trans. on Fuzzy Sets, 2(2), 1994: 119-133.
【28】李少远等．Sugeno 模糊模型的辨识与控制 [J]．自动化学报，24 (4)，1999：488-492．
【29】Sugeno M, Yasukawa T. A fuzzy logical based approach to qualitative modeling [J]. IEEE Trans. on Fuzzy Sets, 1(1), 1993: 7-25.
【30】Wang L X, Mendel J M. Fuzzy basis function, universal approximation and orthogonal least squares learning [J], IEEE Trans. On Neural Networks, 1992, 3(5), 807-814.
【31】Liu K, Lewis F L. Some issues about fuzzy logical control. Proc. of 32nd Conf. Decision and Control, San Antonio, 1993: 1743-1748.
【32】Decarlo R A, Multivariable Nyquist theory[J], International Journal on Control, 25(3), 1977: 234-245.
【33】窦振中，模糊逻辑控制技术及其应用．北京航空航天大学出版
社，1995．
【34】张良杰等，智能控制的模糊神经技术的研究和展望，电子学报，(8)，1995．
【35】Isidori A. Nonlinear Control System, Berlin: Springer-Verlag, 1989.
【36】Kiszka J, Gupta M and Niliforuk P. Energetistic stability of fuzzy dynamic systems, IEEE Trans. System, Man and Cybern, 1985, SMC-15(5): 783-792.
【37】Lapedes A and Farber R. Nonlinear signal processing using neural networks prediction and system modeling. LA-UK-87-2662, 1987.
【38】Luenberger D G. Linear and Nonlinear programming. Addison-Wesley Publishing Company. Inc., 1984.
【39】Sastry S and Bodson M. Adptive Control: Stability, Convergence and Robustness. Englewood Cliffs, NJ: prentic-Hall, 1989.
【40】Slotine J E and Li W. Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice-Hall, Inc., 1991.
【41】Wang L X and Mendel J M. Three-dmensional structured networks for matrix equation solving. IEEE Trans. on Computer, 40(12), 1991: 1337-1346.
【42】《模糊自适应控制理论及其应用》张化光，何希勤等著。北京航空航天大学出版社，2002．
【43】Yah Shi, Masaharu Mizumoto. Some Considerations on Conventional Neural-fuzzy Learning algorithms by gradient descent method. Fuzzy Sets and Systems, 112, 2000: 51-63.
【44】Chyi-Tsong Chen, Shih-Tein Peng. Intelligent process control using neural fuzzy techniques. Journal of Process Control, 9, 1999:
493-503.
【45】Tomohiro takagi and Michio Sugeno, Fuzzy Identification of Systems and Its Applications to Modeling and Control. IEEE Tran. on Systems, Man, and Cybernetic, SMC-15, 1, Jauary/Feberuary 1985: 116-132.
【46】Najib Essounbonli, Abdelaziz Hamzaoui, Janan Zayton. A supervisory Robust adaptive fuzzy controller. Copyright@2002 IFAC 15~(th) Triennial World Congress, Barcelona, Spain.
【47】孙维，王伟，基于T-S模糊模型的非线性系统多模型直接自适应控制。控制与决策，18 (2)，2003：177-180．
【48】Wang L X. Stable Adaptive Fuzzy Controllers with Application to Inverted Pendulum Tracking. IEEE Tran On Systems Man, and Cybernetics-Part B: Cybernetics, 26(5), 1996: 677-691.
【49】张恩勤，施颂椒，高卫华，翁正新．模糊控制系统近年来的研究和发展．控制理论与应用，18 (1)，2001：7-1
【2】王立新。自适应模糊系统与控制—设计与稳定性分析[M]．北京国防工业出版社．
【3】Jin Ⅰ. Et al. Adaptive tracking of SISO nonlinear systems using multi-layered neural networks [J], IEEE Trans. on Neural Networks, 1(1), 1990: 4-27.
【4】Zadeh L. A. Fuzzy Set [M]. Information and Control, 8(3), 1965: 338-358.
【5】张化光．复杂系统的模糊辨识与模糊自适应控制[M]．沈阳：东北大学出版社，1993．
【6】Procyk T. J., Mamdani E. H. A linguistic self-organizing processes controller [J]. Automatica, 15(1), 1979: 15-30.
【7】Chung B. M., Oh J. H. Auto-tuning method of membership function in a fuzzy learning controller [J], journal of Intelligent and Fuzzy Systems, 1(4), 1994: 335-349.
【8】Wang L. X., Stable adaptive fuzzy control of nonlinear Systems [J], IEEE Trans. Fuzzy Syst. 1(2), 1993: t46-155.
【9】Zhang Y. Q, Kandel A. Compensatory neurofuzzy systems with fast learning algorithms [j]. IEEE Trans. on Neural Networks, 9(1), 1998: 83-105.
【10】Zhang J, Morris A. J. Recurrent Neuro-Fuzzy Networks for Nonlinear Process Modeling, IEEE Trans. on Neural Networks, 10(2), 1999: 313-326.
【11】Lee K M, Lwak D H, Kwang H L. Fuzzy Inference Neural Network for Fuzzy Model Tuning, IEEE Trans. on Systems, Man, and Cybernetics-Part B: Cybernetics, 26(4), 1996: 637-645.
【12】鲍鸿，黄心汉，李锡雄．广义模糊推理与广义模糊RBF神经网络[J]，控制与决策，15 (2)，2000：205-208．
【13】张昊，吴捷，郁滨．应用模糊神经网络进行负荷预测的研究[J]，自动化学报，25 (1)，1999：60-67．
【14】孙增圻，张再兴，邓志东．智能控制理论与技术[M]．北京：清华大学出版社，1997：170-180．
【15】Jang S R. ANFIS: Adaptive-network-based fuzzy inference system [J], IEEE Trans. on Systems, Man& Cybernetics, 23(3), 1993: 665-685.
【16】Wang L X, Mendel J M. Fuzzy basis functions, universal approximation and orthogonal least squares learning [J], IEEE Trans. on Neural Networks, 3(5), 1992: 807-814.
【17】李绍远等．智能控制的新进展[J]．控制与决策，15(1)，2000：1-5．
【18】Broomhead D S, Lowe D. Multivariable functional Interpolation and adaptive networks [J], Complex System, 2(4), 1988: 321-355.
【19】阎平凡，张常水．人工神经网络与模拟进化计算 [M]，清华大学出版社，2000．
【20】李人厚．智能控制理论和方法 [M]，西安电子科技大学出版社，1999．
【21】张立明．人工神经网络的模型及其应用 [M]，北京航空航天大学出版社，1993．
【22】陈燕庆．人工神经元网络在控制工程中的应用 [M]，西北工业大学出版社，1991．
【23】Chao C T, Chen Y J, Teng C C. Simplification of Fuzzy-Neural
System Using Similarity Analysis [J]. IEEE Trans. on Systems, Man and Cybernetics-Part B: Cybernetics, 26(3), 1996: 344-354,
【24】周志坚，毛宗源．一种最优模糊神经网络控制器 [J]．控制与决策，15(3)，2000：358—361．
【25】王震雷，顾树生，基于实值遗传算法的模糊神经网络辨识器，东北大学学报(自然科学版)，21 (4)，2000：354-356．
【26】Cao S G, Rees N W. Analysis and design for a class of complex control systems Part Ⅰ: Fuzzy modeling and identification [J]. Automatica, 33(11), 1997: 1017-1028.
【27】Takagi T, Sugeno M. A robust stabilization problem of fuzzy control systems and its application to backing up control of truck-trailer [J]. IEEE Trans. on Fuzzy Sets, 2(2), 1994: 119-133.
【28】李少远等．Sugeno 模糊模型的辨识与控制 [J]．自动化学报，24 (4)，1999：488-492．
【29】Sugeno M, Yasukawa T. A fuzzy logical based approach to qualitative modeling [J]. IEEE Trans. on Fuzzy Sets, 1(1), 1993: 7-25.
【30】Wang L X, Mendel J M. Fuzzy basis function, universal approximation and orthogonal least squares learning [J], IEEE Trans. On Neural Networks, 1992, 3(5), 807-814.
【31】Liu K, Lewis F L. Some issues about fuzzy logical control. Proc. of 32nd Conf. Decision and Control, San Antonio, 1993: 1743-1748.
【32】Decarlo R A, Multivariable Nyquist theory[J], International Journal on Control, 25(3), 1977: 234-245.
【33】窦振中，模糊逻辑控制技术及其应用．北京航空航天大学出版
社，1995．
【34】张良杰等，智能控制的模糊神经技术的研究和展望，电子学报，(8)，1995．
【35】Isidori A. Nonlinear Control System, Berlin: Springer-Verlag, 1989.
【36】Kiszka J, Gupta M and Niliforuk P. Energetistic stability of fuzzy dynamic systems, IEEE Trans. System, Man and Cybern, 1985, SMC-15(5): 783-792.
【37】Lapedes A and Farber R. Nonlinear signal processing using neural networks prediction and system modeling. LA-UK-87-2662, 1987.
【38】Luenberger D G. Linear and Nonlinear programming. Addison-Wesley Publishing Company. Inc., 1984.
【39】Sastry S and Bodson M. Adptive Control: Stability, Convergence and Robustness. Englewood Cliffs, NJ: prentic-Hall, 1989.
【40】Slotine J E and Li W. Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice-Hall, Inc., 1991.
【41】Wang L X and Mendel J M. Three-dmensional structured networks for matrix equation solving. IEEE Trans. on Computer, 40(12), 1991: 1337-1346.
【42】《模糊自适应控制理论及其应用》张化光，何希勤等著。北京航空航天大学出版社，2002．
【43】Yah Shi, Masaharu Mizumoto. Some Considerations on Conventional Neural-fuzzy Learning algorithms by gradient descent method. Fuzzy Sets and Systems, 112, 2000: 51-63.
【44】Chyi-Tsong Chen, Shih-Tein Peng. Intelligent process control using neural fuzzy techniques. Journal of Process Control, 9, 1999:
493-503.
【45】Tomohiro takagi and Michio Sugeno, Fuzzy Identification of Systems and Its Applications to Modeling and Control. IEEE Tran. on Systems, Man, and Cybernetic, SMC-15, 1, Jauary/Feberuary 1985: 116-132.
【46】Najib Essounbonli, Abdelaziz Hamzaoui, Janan Zayton. A supervisory Robust adaptive fuzzy controller. Copyright@2002 IFAC 15~(th) Triennial World Congress, Barcelona, Spain.
【47】孙维，王伟，基于T-S模糊模型的非线性系统多模型直接自适应控制。控制与决策，18 (2)，2003：177-180．
【48】Wang L X. Stable Adaptive Fuzzy Controllers with Application to Inverted Pendulum Tracking. IEEE Tran On Systems Man, and Cybernetics-Part B: Cybernetics, 26(5), 1996: 677-691.
【49】张恩勤，施颂椒，高卫华，翁正新．模糊控制系统近年来的研究和发展．控制理论与应用，18 (1)，2001：7-1