Robust Neural Control of Discrete Time Uncertain Nonlinear Systems Using Sliding Mode Backpropagation Training Algorithm
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摘要
This work deals with robust inverse neural control strategy for a class of single-input single-output(SISO) discrete-time nonlinear system affected by parametric uncertainties. According to the control scheme, in the first step, a direct neural model(DNM)is used to learn the behavior of the system, then, an inverse neural model(INM) is synthesized using a specialized learning technique and cascaded to the uncertain system as a controller. In previous works, the neural models are trained classically by backpropagation(BP) algorithm. In this work, the sliding mode-backpropagation(SM-BP) algorithm, presenting some important properties such as robustness and speedy learning, is investigated. Moreover, four combinations using classical BP and SM-BP are tested to determine the best configuration for the robust control of uncertain nonlinear systems. Two simulation examples are treated to illustrate the effectiveness of the proposed control strategy.
This work deals with robust inverse neural control strategy for a class of single-input single-output(SISO) discrete-time nonlinear system affected by parametric uncertainties. According to the control scheme, in the first step, a direct neural model(DNM)is used to learn the behavior of the system, then, an inverse neural model(INM) is synthesized using a specialized learning technique and cascaded to the uncertain system as a controller. In previous works, the neural models are trained classically by backpropagation(BP) algorithm. In this work, the sliding mode-backpropagation(SM-BP) algorithm, presenting some important properties such as robustness and speedy learning, is investigated. Moreover, four combinations using classical BP and SM-BP are tested to determine the best configuration for the robust control of uncertain nonlinear systems. Two simulation examples are treated to illustrate the effectiveness of the proposed control strategy.
This work deals with robust inverse neural control strategy for a class of single-input single-output(SISO) discrete-time nonlinear system affected by parametric uncertainties. According to the control scheme, in the first step, a direct neural model(DNM)is used to learn the behavior of the system, then, an inverse neural model(INM) is synthesized using a specialized learning technique and cascaded to the uncertain system as a controller. In previous works, the neural models are trained classically by backpropagation(BP) algorithm. In this work, the sliding mode-backpropagation(SM-BP) algorithm, presenting some important properties such as robustness and speedy learning, is investigated. Moreover, four combinations using classical BP and SM-BP are tested to determine the best configuration for the robust control of uncertain nonlinear systems. Two simulation examples are treated to illustrate the effectiveness of the proposed control strategy.
引文
[1]Z.D.Wang,D.W.C.Ho,Y.R.Liu,X.H.Liu.Robust H∞control for a class of nonlinear discrete time-delay stochastic systems with missing measurements.Automatica,vol.45,no.3,pp.684-691,2009.
[2]L.H.Xie.Output feedback H∞control of systems with parameter uncertainty.International Journal of Control,vol.63,no.4,pp.741-750,1996.
[3]S.S.Ge,J.Wang.Robust adaptive tracking for timevarying uncertain nonlinear systems with unknown control coefficients.IEEE Transactions on Automatic Control,vol.48,no.8,pp.1463-1469,2003.
[4]W.M.Haddad,T.Hayakawa,V.Chellaboina.Robust adaptive control for nonlinear uncertain systems.Automatica,vol.39,no.3,pp.551-556,2003.
[5]D.L.Marruedo,T.Alamo,E.F.Camacho.Input-to-state stable MPC for constrained discrete-time nonlinear systems with bounded additive uncertainties.In Proceedings of the41st IEEE Conference on Decision and Control,IEEE,Las Vegas,USA,pp.4619-4624,2002.
[6]D.L.Marruedo1,J.M.Bravo,T.Alamo,E.F.Camacho.Robust MPC of constrained discrete-time nonlinear systems based on uncertain evolution sets:Application to a CSTRmodel.In Proceedings of International Conference on Control Applications,IEEE,Glasgow,UK,pp.657-662,2002.
[7]X.Y.Lu,S.K.Spurgeon.Robust sliding mode control of uncertain nonlinear systems.Systems&Control Letters,vol.32,no.2,pp.75-90,1997.
[8]Y.Q.Xia,Z.Zhu,C.M.Li,H.J.Yang,Q.M.Zhu.Robust adaptive sliding mode control for uncertain discrete-time systems with time delay.Journal of the Franklin Institute,vol.347,no.1,pp.339-357,2010.
[9]J.J.Garside,T.L.Ruchti,R.H.Brown.Using selforganizing artificial neural networks for solving uncertain dynamic nonlinear system identification and function modeling problems.In Proceedings of the 31st IEEE Conference on Decision and Control,IEEE,Tucson,USA,pp.2716-2721,1992.
[10]R.H.Brown,T.L.Ruchti,X.Feng.Artificial neural network identification of partially known dynamic nonlinear systems.In Proceedings of the 32nd IEEE Conference on Decision and Control,IEEE,USA,pp.3694-3699,1993.
[11]T.Tsuji,B.H.Xu,M.Kaneko.Adaptive control and identification using one neural network for a class of plants with uncertainties.IEEE Transactions on Systems,Man,and Cybernetics Part A:Systems and Humans,vol.28,no.4,pp.496-505,1998.
[12]A V.Topalov,O.Kaynak.Robust neural identification of robotic manipulators using discrete time adaptive sliding mode learning.In Proceedings of the 16th IFAC World Congress,IFAC,Czech Republic,2005.
[13]Y.J.Shu,X.Liu,Y.J.Liu.Stability and passivity analysis for uncertain discrete-time neural networks with timevarying delay.Neurocomputing,vol.173,pp.1706-1714,2016.
[14]X.Wang,T.S.Li,C.L.Philip Chen,B.Lin.Adaptive robust control based on single neural network approximation for a class of uncertain strict-feedback discrete-time nonlinear systems.Neurocomputing,vol.138,pp.325-331,2014.
[15]Y.J.Liu,S.C.Tong.Adaptive NN tracking control of uncertain nonlinear discrete-time systems with nonaffine deadzone input.IEEE Transactions on Cybernetics,vol.45,no.3,pp.497-505,2015.
[16]Y.J.Liu,L.Tang,S.C.Tong,C.L.Philip Chen,D.J.Li.Reinforcement learning design-based adaptive tracking control with less learning parameters for nonlinear discretetime MIMO systems.IEEE Transactions on Neural Networks and Learning Systems,vol.26,no.1,pp.165-176,2015.
[17]M.Chen,S.S.Ge,B.V.E.How.Robust adaptive neural network control for a class of uncertain MIMO nonlinear systems with input nonlinearities.IEEE Transactions on Neural Networks,vol.21,no.5,pp.796-812,2010.
[18]Q.G.Li,S.C.Tong,T.Y.Chai.H∞tracking of unknown nonlinear systems using neural network.In Proceedings of International Symposium on Intelligent Control,IEEE,Istanbul,pp.199-204,1997.
[19]W.Y.Wang,M.L.Chan,C.C.J.Hsu,T.T.Lee.H∞tracking-based sliding mode control for uncertain nonlinear systems via an adaptive fuzzy-neural approach.IEEETransactions on Systems,Man,and Cybernetics,vol.32,no.4,pp.483-492,2002.
[20]H.Deng,Z.Xu,H.X.Li.A novel neural internal model control for multi-input multi-output nonlinear discretetime processes.Journal of Process Control,vol.19,no.8,pp.1392-1400,2009.
[21]K.S.Narendra,K.Parthasarathy.Identification and control of dynamical systems using neural networks.IEEETransactions on Neural Networks,vol.1,no.1,pp.4-27,1990.
[22]F.Cubillos,H.Callejas,E.L.Lima,M.P.Vega.Adaptive control using a hybrid-neural model:Application to a polymerisation reactor.Brazilian Journal of Chemical Engineering,vol.18,no.1,pp.113-120,2001.
[23]D.E.Rumelhart,G.E.Hinton,R.J.Williams.Learning internal representations by error propagation.Parallel Distributed Processing:Explorations in the Microstructure of Cognition,Cambridge,USA:MIT Press,pp.318-362,1986.
[24]Q.Song,J.Z.Xiao,Y.C.Soh.Robust backpropagation training algorithm for multilayered neural tracking controller.IEEE Transactions on Neural Networks,vol.10,no.5,pp.1133-1141,1999.
[25]C.C.Chuang,S.F.Su,C.C.Hsiao.The annealing robust backpropagation(ARBP)learning algorithm.IEEE Transactions on Neural Networks,vol.11,no.5,pp.1067-1077,2000.
[26]A.Rusiecki.Robust MCD-based backpropagation learning algorithm.In Proceedings of the 9th International Conference on Artifical Intelligence and Soft Computing,Lecture Notes in Computer Science,Springer,Zakopane,Poland,vol.5097,pp.154-163,2008.
[27]A.Rusiecki.Fast robust learning algorithm dedicated to LMLS criterion.In Proceedings of the 10th International Conference on Artifical Intelligence and Soft Computing,Lecture Notes in Computer Science,Springer,Zakopane,Poland,vol.6114,pp.96-103,2010.
[28]A.Nied,S.I.Seleme,Jr.,G.G.Parma,B.R.Menezes.Online neural training algorithm with sliding mode control and adaptive learning rate.Neurocomputing,vol.70,no.16-18,pp.2687-2691,2007.
[29]H.Sira-Ramirez,E.Colina-Morles.A sliding mode strategy for adaptive learning in Adalines.IEEE Transactions on Circuits and Systems-I:Fundamental Theory and Applications,vol.42,no.12,pp.1001-1012,1995.
[30]X.H.Yu,Z.H.Ma,S.M.M.Rahman.Adaptive sliding mode approach for learning in a feedforward neural network.Neural Computing and Applications,vol.7,no.4,pp.289-294,1998.
[31]A.V.Topalov,O.Kaynak.A sliding mode strategy for adaptive learning in multilayer feedforward neural networks with a scalar output.In Proceedings of IEEE International Conference on Systems,Man and Cybernetics,IEEE,Washington,USA,pp.1636-1641,2003.
[32]A.V.Topalov,O.Kaynak,N.G.Shakev.Variable structure systems approach for on-line learning in multilayer artificial neural networks.In Proceedings of the 29th Annual Conference of the IEEE Industrial Electronics Society,IEEE,Roanoke,USA,pp.2989-2994,2003.
[33]G.G.Parma,B.R.Menezes,A.P.Barga.Sliding mode algorithm for training multilayer artificial neural networks.Electronics Letters,vol.34,no.1,pp.97-98,1998.
[34]G.G.Parma,B.R.Menezes,A.P.Barga.Improving backpropagation with sliding mode control.In Proceedings of the 5th Brazilian Symposium on Neural Networks,IEEE,Belo Horizonte,Brazil,pp.8-13,1998.
[35]V.I.Utkin.Sliding Modes and Their Application in Variable Structure Systems,Moscow,RUssia:MIR,1978.
[36]A.V.Topalov,O.Kaynak.Neural network modeling and control of cement mills using a variable structure systems theory based on-line learning mechanism.Journal of Process Control,vol.14,no.5,pp.581-589,2004.
[37]S.Sarpturk,Y.Istefanopulos,O.Kaynak.On the stability of discrete-time sliding mode control systems.IEEE Transactions on Automatic Control,vol.32,no.10,pp.930-932,1987.
[38]G.G.Parma,B.R.Menezes,A.P.Barga.Sliding mode backpropagation:Control theory applied to neural network learning.In Proceedings of the International Joint Conference on Neural Networks,IEEE,Washington,USA,pp.1774-1778,1999.
[39]D.Psaltis,A.Sideris,A.A.Yamamura.A multilayered neural network controller.IEEE Control Systems Magazine,vol.8,no.2,pp.17-21,1988.
[40]S.Aoughellanet,T.Mohammedi,Y.Bouterfa.Reduced neural network models for dynamical systems.In Proceedings of the 6th WSEAS International Conference on Neural Networks,WSEAS,Lisbon,Portugal,pp.26-29,2005.
[41]K.M.Passino,S.Yurkovich.Fuzzy Control,Menlo Park,CA:Addison-Wesley Longman,1998.
[42]K.M.Passino.Biomimicry for Optimization,Control,and Automation,London,UK:Springer-Verlag,2005.
[2]L.H.Xie.Output feedback H∞control of systems with parameter uncertainty.International Journal of Control,vol.63,no.4,pp.741-750,1996.
[3]S.S.Ge,J.Wang.Robust adaptive tracking for timevarying uncertain nonlinear systems with unknown control coefficients.IEEE Transactions on Automatic Control,vol.48,no.8,pp.1463-1469,2003.
[4]W.M.Haddad,T.Hayakawa,V.Chellaboina.Robust adaptive control for nonlinear uncertain systems.Automatica,vol.39,no.3,pp.551-556,2003.
[5]D.L.Marruedo,T.Alamo,E.F.Camacho.Input-to-state stable MPC for constrained discrete-time nonlinear systems with bounded additive uncertainties.In Proceedings of the41st IEEE Conference on Decision and Control,IEEE,Las Vegas,USA,pp.4619-4624,2002.
[6]D.L.Marruedo1,J.M.Bravo,T.Alamo,E.F.Camacho.Robust MPC of constrained discrete-time nonlinear systems based on uncertain evolution sets:Application to a CSTRmodel.In Proceedings of International Conference on Control Applications,IEEE,Glasgow,UK,pp.657-662,2002.
[7]X.Y.Lu,S.K.Spurgeon.Robust sliding mode control of uncertain nonlinear systems.Systems&Control Letters,vol.32,no.2,pp.75-90,1997.
[8]Y.Q.Xia,Z.Zhu,C.M.Li,H.J.Yang,Q.M.Zhu.Robust adaptive sliding mode control for uncertain discrete-time systems with time delay.Journal of the Franklin Institute,vol.347,no.1,pp.339-357,2010.
[9]J.J.Garside,T.L.Ruchti,R.H.Brown.Using selforganizing artificial neural networks for solving uncertain dynamic nonlinear system identification and function modeling problems.In Proceedings of the 31st IEEE Conference on Decision and Control,IEEE,Tucson,USA,pp.2716-2721,1992.
[10]R.H.Brown,T.L.Ruchti,X.Feng.Artificial neural network identification of partially known dynamic nonlinear systems.In Proceedings of the 32nd IEEE Conference on Decision and Control,IEEE,USA,pp.3694-3699,1993.
[11]T.Tsuji,B.H.Xu,M.Kaneko.Adaptive control and identification using one neural network for a class of plants with uncertainties.IEEE Transactions on Systems,Man,and Cybernetics Part A:Systems and Humans,vol.28,no.4,pp.496-505,1998.
[12]A V.Topalov,O.Kaynak.Robust neural identification of robotic manipulators using discrete time adaptive sliding mode learning.In Proceedings of the 16th IFAC World Congress,IFAC,Czech Republic,2005.
[13]Y.J.Shu,X.Liu,Y.J.Liu.Stability and passivity analysis for uncertain discrete-time neural networks with timevarying delay.Neurocomputing,vol.173,pp.1706-1714,2016.
[14]X.Wang,T.S.Li,C.L.Philip Chen,B.Lin.Adaptive robust control based on single neural network approximation for a class of uncertain strict-feedback discrete-time nonlinear systems.Neurocomputing,vol.138,pp.325-331,2014.
[15]Y.J.Liu,S.C.Tong.Adaptive NN tracking control of uncertain nonlinear discrete-time systems with nonaffine deadzone input.IEEE Transactions on Cybernetics,vol.45,no.3,pp.497-505,2015.
[16]Y.J.Liu,L.Tang,S.C.Tong,C.L.Philip Chen,D.J.Li.Reinforcement learning design-based adaptive tracking control with less learning parameters for nonlinear discretetime MIMO systems.IEEE Transactions on Neural Networks and Learning Systems,vol.26,no.1,pp.165-176,2015.
[17]M.Chen,S.S.Ge,B.V.E.How.Robust adaptive neural network control for a class of uncertain MIMO nonlinear systems with input nonlinearities.IEEE Transactions on Neural Networks,vol.21,no.5,pp.796-812,2010.
[18]Q.G.Li,S.C.Tong,T.Y.Chai.H∞tracking of unknown nonlinear systems using neural network.In Proceedings of International Symposium on Intelligent Control,IEEE,Istanbul,pp.199-204,1997.
[19]W.Y.Wang,M.L.Chan,C.C.J.Hsu,T.T.Lee.H∞tracking-based sliding mode control for uncertain nonlinear systems via an adaptive fuzzy-neural approach.IEEETransactions on Systems,Man,and Cybernetics,vol.32,no.4,pp.483-492,2002.
[20]H.Deng,Z.Xu,H.X.Li.A novel neural internal model control for multi-input multi-output nonlinear discretetime processes.Journal of Process Control,vol.19,no.8,pp.1392-1400,2009.
[21]K.S.Narendra,K.Parthasarathy.Identification and control of dynamical systems using neural networks.IEEETransactions on Neural Networks,vol.1,no.1,pp.4-27,1990.
[22]F.Cubillos,H.Callejas,E.L.Lima,M.P.Vega.Adaptive control using a hybrid-neural model:Application to a polymerisation reactor.Brazilian Journal of Chemical Engineering,vol.18,no.1,pp.113-120,2001.
[23]D.E.Rumelhart,G.E.Hinton,R.J.Williams.Learning internal representations by error propagation.Parallel Distributed Processing:Explorations in the Microstructure of Cognition,Cambridge,USA:MIT Press,pp.318-362,1986.
[24]Q.Song,J.Z.Xiao,Y.C.Soh.Robust backpropagation training algorithm for multilayered neural tracking controller.IEEE Transactions on Neural Networks,vol.10,no.5,pp.1133-1141,1999.
[25]C.C.Chuang,S.F.Su,C.C.Hsiao.The annealing robust backpropagation(ARBP)learning algorithm.IEEE Transactions on Neural Networks,vol.11,no.5,pp.1067-1077,2000.
[26]A.Rusiecki.Robust MCD-based backpropagation learning algorithm.In Proceedings of the 9th International Conference on Artifical Intelligence and Soft Computing,Lecture Notes in Computer Science,Springer,Zakopane,Poland,vol.5097,pp.154-163,2008.
[27]A.Rusiecki.Fast robust learning algorithm dedicated to LMLS criterion.In Proceedings of the 10th International Conference on Artifical Intelligence and Soft Computing,Lecture Notes in Computer Science,Springer,Zakopane,Poland,vol.6114,pp.96-103,2010.
[28]A.Nied,S.I.Seleme,Jr.,G.G.Parma,B.R.Menezes.Online neural training algorithm with sliding mode control and adaptive learning rate.Neurocomputing,vol.70,no.16-18,pp.2687-2691,2007.
[29]H.Sira-Ramirez,E.Colina-Morles.A sliding mode strategy for adaptive learning in Adalines.IEEE Transactions on Circuits and Systems-I:Fundamental Theory and Applications,vol.42,no.12,pp.1001-1012,1995.
[30]X.H.Yu,Z.H.Ma,S.M.M.Rahman.Adaptive sliding mode approach for learning in a feedforward neural network.Neural Computing and Applications,vol.7,no.4,pp.289-294,1998.
[31]A.V.Topalov,O.Kaynak.A sliding mode strategy for adaptive learning in multilayer feedforward neural networks with a scalar output.In Proceedings of IEEE International Conference on Systems,Man and Cybernetics,IEEE,Washington,USA,pp.1636-1641,2003.
[32]A.V.Topalov,O.Kaynak,N.G.Shakev.Variable structure systems approach for on-line learning in multilayer artificial neural networks.In Proceedings of the 29th Annual Conference of the IEEE Industrial Electronics Society,IEEE,Roanoke,USA,pp.2989-2994,2003.
[33]G.G.Parma,B.R.Menezes,A.P.Barga.Sliding mode algorithm for training multilayer artificial neural networks.Electronics Letters,vol.34,no.1,pp.97-98,1998.
[34]G.G.Parma,B.R.Menezes,A.P.Barga.Improving backpropagation with sliding mode control.In Proceedings of the 5th Brazilian Symposium on Neural Networks,IEEE,Belo Horizonte,Brazil,pp.8-13,1998.
[35]V.I.Utkin.Sliding Modes and Their Application in Variable Structure Systems,Moscow,RUssia:MIR,1978.
[36]A.V.Topalov,O.Kaynak.Neural network modeling and control of cement mills using a variable structure systems theory based on-line learning mechanism.Journal of Process Control,vol.14,no.5,pp.581-589,2004.
[37]S.Sarpturk,Y.Istefanopulos,O.Kaynak.On the stability of discrete-time sliding mode control systems.IEEE Transactions on Automatic Control,vol.32,no.10,pp.930-932,1987.
[38]G.G.Parma,B.R.Menezes,A.P.Barga.Sliding mode backpropagation:Control theory applied to neural network learning.In Proceedings of the International Joint Conference on Neural Networks,IEEE,Washington,USA,pp.1774-1778,1999.
[39]D.Psaltis,A.Sideris,A.A.Yamamura.A multilayered neural network controller.IEEE Control Systems Magazine,vol.8,no.2,pp.17-21,1988.
[40]S.Aoughellanet,T.Mohammedi,Y.Bouterfa.Reduced neural network models for dynamical systems.In Proceedings of the 6th WSEAS International Conference on Neural Networks,WSEAS,Lisbon,Portugal,pp.26-29,2005.
[41]K.M.Passino,S.Yurkovich.Fuzzy Control,Menlo Park,CA:Addison-Wesley Longman,1998.
[42]K.M.Passino.Biomimicry for Optimization,Control,and Automation,London,UK:Springer-Verlag,2005.