一类不确定非线性离散系统的模糊自适应控制器设计
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摘要
针对一类不确定非线性离散系统,提出一种带有自动可调伸缩因子的模糊自适应控制方法.该控制器设计方法的优点是模糊逻辑系统的逼近精度不再依赖于模糊逻辑系统的结构和规则数目,参数自适应律调节与被逼近函数的特征和逼近精度有关,因此能有效减少在线估计的参数数目,且设计方法能够保证闭环系统的所有状态半全局一致终极有界.最后,通过数值仿真算例表明所提出方法的有效性.
A fuzzy adaptive controller with scaler is proposed for a class of uncertain nonlinear discrete-time systems in this paper. The advantage of the design method is that the approximation of fuzzy logic systems does not depend on the structure and the number of the rules in fuzzy logic systems, and the number of updated laws is related to the character and approximation of the approximated functions, which can not only reduce the number of on-line parameters, but also guarantee the states of systems semi-global uniformly ultimately bounded(UUB). Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
A fuzzy adaptive controller with scaler is proposed for a class of uncertain nonlinear discrete-time systems in this paper. The advantage of the design method is that the approximation of fuzzy logic systems does not depend on the structure and the number of the rules in fuzzy logic systems, and the number of updated laws is related to the character and approximation of the approximated functions, which can not only reduce the number of on-line parameters, but also guarantee the states of systems semi-global uniformly ultimately bounded(UUB). Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
引文
[1] Wang L X. Stable adaptive fuzzy control of nonlinear systems[J]. IEEE Trans on Fuzzy Systems, 1993, 1(2):146-155.
[2] Castro J L. Fuzzy logic controllers are universal approximators[J]. IEEE Trans on Systems, Man,Cybernetics, 1995, 25(4):629-635.
[3]秦勇,贾利民,张锡第.基于广义模糊基函数的多变量模糊模型及其辨识方法[J].控制与决策, 1997, 12(增):491-495.(Qin Y, Jia L M, Zhang X D. Multivariable fuzzy system model using generalized fuzzy basis function and its identification method[J]. Control and Decision, 1997,12(S):491-495.)
[4] Chai T Y, Tong S C. Fuzzy direct adaptive control for a class of nonlinear systems[J]. Fuzzy Sets and Systems,1999, 103(3):379-387.
[5] Wang L X. A course in fuzzy system and control[M].Prentice-Hall:Upper Saddle River, 1997:172-175.
[6] Wang F, Liu Z, Lai G. Fuzzy adaptive control of nonlinear uncertain plants with unknown dead zone output[J].Fuzzy Sets and Systems, 2015, 263(1):27-48.
[7] Liu Yanjun, Tang Li, Tong Shaocheng, et al.Reinforcement learning design-based adaptive tracking control with less learning parameters for nonlinear discrete-time MIMO systems[J]. IEEE Trans on Neural Networks and Learning Systems, 2015, 26(1):165-176.
[8] Liu Yanjun, Li Jing, Tong Shaocheng, et al. Neural network control-based adaptive learning design for nonlinear systems with full-state constrains[J]. IEEE Trans on Neural Networks and Learning Systems, 2016,27(7):1562-1571.
[9] Liu Lei, Wang Zhanshan, Zhang Huaguang. Adaptive fault-tolerant tracking control for MIMO discrete-time systems via reinforcement learning algorithm with less learning parameters[J]. IEEE Trans on Automation Science and Engineering, 2017, 14(1):299-313.
[10]刘晓华,解学军,冯恩民.不需持续激励条件的非线性离散时间系统的自适应模糊逻辑控制[J].控制与决策, 2002, 17(3):269-273.(Liu X H, Xie X J, Feng E M. Adaptive fuzzy logic control of nonlinear discrete-time systems without the persistent excitation condition[J]. Control and Decision,2002, 17(3):269-273.)
[11] Boulkroune A, Tradjine M, Saad M M, et al. Design of a unified adaptive fuzzy observer for uncertain nonlinear systems[J]. Information Science, 2014, 265:139-153.
[12]王佐伟,吴宏鑫.非线性离散时间系统的自适应模糊补偿控制[J].控制与决策, 2005, 20(2):147-151.(Wang Z W, Wu H X. Adaptive fuzzy logic compensation control for nonlinear discrete-time systems[J]. Control and Decision, 2005, 20(2):147-151.)
[13] Gao Y, Liu Y J. Adaptive fuzzy optimal control using direct heuristic dynamic programming for chaotic discrete-time system[J]. J of Vibration and Control, 2016,22(2):595-603.
[18] Li H, Wang J, Shi P. Output-feedback based sliding mode control for fuzzy systems with actuator saturation[J].IEEE Trans on Fuzzy Systems, 2016, 24(6):1282-1293.
[15] Tong S C, He X L, Zhang H G. A combined backstepping and small-gain approach to robust adaptive fuzzy output feedback control[J]. IEEE Trans on Fuzzy Systems, 2010,17(5):1059-1069.
[16] Lai G, Liu Z, Zhang Y, et al. Adaptive fuzzy quantized control of time-delayed nonlinear systems with communication constraint[J]. Fuzzy Sets and Systems,2017, 314(1):61-78.
[17] Mekircha N, Boukabou A, Mansouri N. Fuzzy control of original UPOs of unknown discrete chaotic systems[J]. Applied Mathematical Modelling, 2012,36(10):5135-5142.
[18] Chen W S, Jiao L C, Li R H, et al. Adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances[J]. IEEE Trans on Fuzzy Systems,2010, 18(4):674-685.
[19] Liu Y J, Wang W, Tong S C, et al. Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters[J]. IEEE Trans on Systems,Man, and Cybernetics, Part A:Systems and Humans,2010, 40(1):170-184.
[20] Chen B, Liu X P, Lin C. Direct adaptive fuzzy control of nonlinear strict-feedback systems[J]. Automatica, 2009,45(6):1350-1355.
[21] Wang H, Wang Z F, Liu Y J, et al. Fuzzy tracking adaptive control of discrete-time switched nonlinear systems[J].Fuzzy Sets and Systems, 2017, 316(1):35-48.
[22] Liu Y J, Gao Y, Tong S C, et al. Fuzzy approximation-based adaptive backstepping optimal control for a class of nonlinear discrete-time systems with dead-zone[J]. IEEE Trans on Fuzzy Systems, 2016, 24(1):16-28.
[23]张化光,王智良,黎明,等.广义模糊双曲正切模型:一个万能逼近器[J].自动化学报, 2004, 30(3):416-422.(Zhang H G, Wang Z L, Li M, et al. Generalized fuzzy hyperbolic model:A universal approximator[J]. Acta Automatica Sinica, 2004, 30(3):416-422.)
[24] Liu Lei, Wang Zhanshan, Huang Zhanjun, et al. Adaptive predefined performance control for MIMO systems with unknown direction via generalized fuzzy hyperbolic model[J]. IEEE Trans on Fuzzy Systems, 2017, 25(3):527-542.
[25] Castro J L, Delgado M. Fuzzy systems with defuzzification are universal approximators[J]. IEEE Trans on Systems, Man, and Cybernetics, Par B:Cybernetics, 1996, 26(1):149-153.
[26]王国俊.非经典数理逻辑与近似推理[M].北京:科学出版社, 2003:93-100.(Wang G J. Nonclassical mathematical logic and approximate reasoning[M]. Beijing:Science Press, 2003:93-100.)
[27] Perfilieva I. Normal forms for fuzzy logic functions and their approximation ability[J]. Fuzzy Sets and Systems,2001, 124(3):372-384.
[28] Vandegrift M, Lewis F L, Jagannathan S, et al.Adaptive fuzzy logic control of discrete-time dynamical systems[C]. Proc IEEE Int Conf on Intelligence Control.San Diego, 1995:395-401.
[29]范永青,王银河,罗亮,等.基于伸缩器和饱和器的一类非线性系统模糊自适应控制设计[J].控制理论与应用, 2011, 28(9):1105-1110.(Fan Y Q, WangY H, Luo L, et al. Fuzzy adaptive control design for a class of nonlinear systems with scalers and saturators[J]. Control Theory&Applications, 2011,28(9):1105-1110.)
[30]郭雷,魏晨.基于LS算法的离散时间非线性系统自适应控制—–可行性及局限[J].中国科学:A辑, 1996,26(4):289-299.(Guo L, Wei C. Feasibility and limitations—Adaptive control of discrete-time nonlinear systems based on LS algorithm[J]. Science in China:Series A, 1996, 26(4):289-299.)
[31] Zemouche A, Boutayeb M. Observers design for discrete-time Lipschitz nonlinear systems, State of the art and new results[C]. The 51st IEEE Conf on Decision and Control. Hawall, 2012:4780-4785.
[32] Zulfiqar A, Rehan M, Abid M. Observer design for one-sided Lipschitz descriptor systems[J]. Applied Mathematical Modelling, 2016, 40(3):2301-2311.
[33] Furuta K. Sliding mode control of a discrete system[J].Systems and Control Letters, 1990, 14(2):145-152.
[2] Castro J L. Fuzzy logic controllers are universal approximators[J]. IEEE Trans on Systems, Man,Cybernetics, 1995, 25(4):629-635.
[3]秦勇,贾利民,张锡第.基于广义模糊基函数的多变量模糊模型及其辨识方法[J].控制与决策, 1997, 12(增):491-495.(Qin Y, Jia L M, Zhang X D. Multivariable fuzzy system model using generalized fuzzy basis function and its identification method[J]. Control and Decision, 1997,12(S):491-495.)
[4] Chai T Y, Tong S C. Fuzzy direct adaptive control for a class of nonlinear systems[J]. Fuzzy Sets and Systems,1999, 103(3):379-387.
[5] Wang L X. A course in fuzzy system and control[M].Prentice-Hall:Upper Saddle River, 1997:172-175.
[6] Wang F, Liu Z, Lai G. Fuzzy adaptive control of nonlinear uncertain plants with unknown dead zone output[J].Fuzzy Sets and Systems, 2015, 263(1):27-48.
[7] Liu Yanjun, Tang Li, Tong Shaocheng, et al.Reinforcement learning design-based adaptive tracking control with less learning parameters for nonlinear discrete-time MIMO systems[J]. IEEE Trans on Neural Networks and Learning Systems, 2015, 26(1):165-176.
[8] Liu Yanjun, Li Jing, Tong Shaocheng, et al. Neural network control-based adaptive learning design for nonlinear systems with full-state constrains[J]. IEEE Trans on Neural Networks and Learning Systems, 2016,27(7):1562-1571.
[9] Liu Lei, Wang Zhanshan, Zhang Huaguang. Adaptive fault-tolerant tracking control for MIMO discrete-time systems via reinforcement learning algorithm with less learning parameters[J]. IEEE Trans on Automation Science and Engineering, 2017, 14(1):299-313.
[10]刘晓华,解学军,冯恩民.不需持续激励条件的非线性离散时间系统的自适应模糊逻辑控制[J].控制与决策, 2002, 17(3):269-273.(Liu X H, Xie X J, Feng E M. Adaptive fuzzy logic control of nonlinear discrete-time systems without the persistent excitation condition[J]. Control and Decision,2002, 17(3):269-273.)
[11] Boulkroune A, Tradjine M, Saad M M, et al. Design of a unified adaptive fuzzy observer for uncertain nonlinear systems[J]. Information Science, 2014, 265:139-153.
[12]王佐伟,吴宏鑫.非线性离散时间系统的自适应模糊补偿控制[J].控制与决策, 2005, 20(2):147-151.(Wang Z W, Wu H X. Adaptive fuzzy logic compensation control for nonlinear discrete-time systems[J]. Control and Decision, 2005, 20(2):147-151.)
[13] Gao Y, Liu Y J. Adaptive fuzzy optimal control using direct heuristic dynamic programming for chaotic discrete-time system[J]. J of Vibration and Control, 2016,22(2):595-603.
[18] Li H, Wang J, Shi P. Output-feedback based sliding mode control for fuzzy systems with actuator saturation[J].IEEE Trans on Fuzzy Systems, 2016, 24(6):1282-1293.
[15] Tong S C, He X L, Zhang H G. A combined backstepping and small-gain approach to robust adaptive fuzzy output feedback control[J]. IEEE Trans on Fuzzy Systems, 2010,17(5):1059-1069.
[16] Lai G, Liu Z, Zhang Y, et al. Adaptive fuzzy quantized control of time-delayed nonlinear systems with communication constraint[J]. Fuzzy Sets and Systems,2017, 314(1):61-78.
[17] Mekircha N, Boukabou A, Mansouri N. Fuzzy control of original UPOs of unknown discrete chaotic systems[J]. Applied Mathematical Modelling, 2012,36(10):5135-5142.
[18] Chen W S, Jiao L C, Li R H, et al. Adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances[J]. IEEE Trans on Fuzzy Systems,2010, 18(4):674-685.
[19] Liu Y J, Wang W, Tong S C, et al. Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters[J]. IEEE Trans on Systems,Man, and Cybernetics, Part A:Systems and Humans,2010, 40(1):170-184.
[20] Chen B, Liu X P, Lin C. Direct adaptive fuzzy control of nonlinear strict-feedback systems[J]. Automatica, 2009,45(6):1350-1355.
[21] Wang H, Wang Z F, Liu Y J, et al. Fuzzy tracking adaptive control of discrete-time switched nonlinear systems[J].Fuzzy Sets and Systems, 2017, 316(1):35-48.
[22] Liu Y J, Gao Y, Tong S C, et al. Fuzzy approximation-based adaptive backstepping optimal control for a class of nonlinear discrete-time systems with dead-zone[J]. IEEE Trans on Fuzzy Systems, 2016, 24(1):16-28.
[23]张化光,王智良,黎明,等.广义模糊双曲正切模型:一个万能逼近器[J].自动化学报, 2004, 30(3):416-422.(Zhang H G, Wang Z L, Li M, et al. Generalized fuzzy hyperbolic model:A universal approximator[J]. Acta Automatica Sinica, 2004, 30(3):416-422.)
[24] Liu Lei, Wang Zhanshan, Huang Zhanjun, et al. Adaptive predefined performance control for MIMO systems with unknown direction via generalized fuzzy hyperbolic model[J]. IEEE Trans on Fuzzy Systems, 2017, 25(3):527-542.
[25] Castro J L, Delgado M. Fuzzy systems with defuzzification are universal approximators[J]. IEEE Trans on Systems, Man, and Cybernetics, Par B:Cybernetics, 1996, 26(1):149-153.
[26]王国俊.非经典数理逻辑与近似推理[M].北京:科学出版社, 2003:93-100.(Wang G J. Nonclassical mathematical logic and approximate reasoning[M]. Beijing:Science Press, 2003:93-100.)
[27] Perfilieva I. Normal forms for fuzzy logic functions and their approximation ability[J]. Fuzzy Sets and Systems,2001, 124(3):372-384.
[28] Vandegrift M, Lewis F L, Jagannathan S, et al.Adaptive fuzzy logic control of discrete-time dynamical systems[C]. Proc IEEE Int Conf on Intelligence Control.San Diego, 1995:395-401.
[29]范永青,王银河,罗亮,等.基于伸缩器和饱和器的一类非线性系统模糊自适应控制设计[J].控制理论与应用, 2011, 28(9):1105-1110.(Fan Y Q, WangY H, Luo L, et al. Fuzzy adaptive control design for a class of nonlinear systems with scalers and saturators[J]. Control Theory&Applications, 2011,28(9):1105-1110.)
[30]郭雷,魏晨.基于LS算法的离散时间非线性系统自适应控制—–可行性及局限[J].中国科学:A辑, 1996,26(4):289-299.(Guo L, Wei C. Feasibility and limitations—Adaptive control of discrete-time nonlinear systems based on LS algorithm[J]. Science in China:Series A, 1996, 26(4):289-299.)
[31] Zemouche A, Boutayeb M. Observers design for discrete-time Lipschitz nonlinear systems, State of the art and new results[C]. The 51st IEEE Conf on Decision and Control. Hawall, 2012:4780-4785.
[32] Zulfiqar A, Rehan M, Abid M. Observer design for one-sided Lipschitz descriptor systems[J]. Applied Mathematical Modelling, 2016, 40(3):2301-2311.
[33] Furuta K. Sliding mode control of a discrete system[J].Systems and Control Letters, 1990, 14(2):145-152.