Email this article Neural Network Adaptive Control for a Class of Matched SISO Nonlinear Uncertain Systems With Zero Dynamics
Abstract
The paper presents a direct adaptive tracking control scheme for a class of matched SISO affine nonlinear uncertain systems with zero dynamic using neural network. Through neural network approximation, neural network is used as the emulator of the unknown ideal controller. A quadratic cost function of the error between the unknown ideal controller and the used neural network controller is minimized using a gradient descent method to adjust parameters in neural network. The convergence of parameters and the uniformly ultimately boundedness of tracking error and all states of the closed-loop system are guaranteed based on Lyapunov stability theorem. The effectiveness of the proposed controller is illustrated through the simulation results.
Keywords
References
[1] Liu G R,Wan B W. “Indirect adaptive fuzy robust control for a class of nonlinear MIMO systems”.Control and Decision,vol.17,pp.676-680,2002.
[2] Tong S C,Qu L J. “Fuzzy adaptive output feedback control for a class of MIMO nonlinear systems”.Control and Decision,vol.27,781-793,2005.
[3] Hu H, Liu G R,Tang H Z,Guo Peng. “Robust output tracking control for mismatched uncertainties nonlinear systems”, Natural Science Journal of Xiangtan University,vol.32,pp.108-111,2010.
[4] Chen W,Wang Y N,Huang H X. “L2 robust control of induction motor based on backstepping”,Natural Science Journal of Xiangtan University,vol.32,pp.106-111,2010.
[5] Salim L, Thierry M G. “Adaptive fuzzy control of a class of SISO nonaffine nonlinear systems”.Fuzzy Sets and Systems,vol.158,pp.1126-1137,2007.
http://dx.doi.org/10.1016/j.fss.2006.11.013
[6] Huang H X,Nuan T. “Application of adaptive fuzzy sliding mode control based on GA in positioning servo system of the permanent magnetic linear motors”, Natural Science Journal of Xiangtan University,vol.32,pp.94-98,2010.
[7] Chang Y C,Yen H M. “Adaptive output feedback tracking control for a class of uncertain nonlinear systems using neural networks”.IEEE Trans on systems,man,and cybernetics-part B:cybernetics,vol. 36,pp.1311-1316,2005.
[8] Sunan N H,Tan K K.T.H.Lee. “Further results on adaptive control for a class of nonlinear systems using neural networks”.IEEE Trans on neural network,vol.14, pp.719-722,2003.
http://dx.doi.org/10.1109/TNN.2003.811712
PMid:18238054
[9] Hu H, Liu G R, Liu D B,Guo P. “Output feedback tracking control for a class of uncertain nonlinear MIMO systems using neural network”.Control Theory&Applications,vol.27,pp.382-386,2010
[10] Ge S S,Zhang J. “Neural-network control of nonaffine nonlinear system with zero dynamics by state and output feedback”.IEEE Transaction on neural networks,vol.14,pp.900-918,2003
http://dx.doi.org/10.1109/TNN.2003.813823
PMid:18238069
[11] W.Hahn, Stability of Motion. Springer Verlag. Berlin,1967
[12] Lin C.M, Chen T.Y. “Self-organizing CMAC control for a class of MIMO uncertain nonlinear systems”, .IEEE Transaction on neural networks,vol.20,pp.1377-1384,2009.
PMid:19398404
[13] S.Blazic,I.Skrjanc,D.Matko “Globally stable direct fuzzy model reference adaptive control”,Fuzzy Sets and Systems,vol.139,pp.3-33,2003.
http://dx.doi.org/10.1016/S0165-0114(02)00479-7
[14] Y.C.Chang, “Robust tracking control for nonlinear MIMO systems via fuzzy approaches”,Automatica,vol.36,pp.1535-1545,2000.
http://dx.doi.org/10.1016/S0005-1098(00)00083-2
[15] Jianming Lian, Yonggon Lee, Stanislaw H.Zak “Variable neural direct adaptive robust control of uncertain systems”,IEEE Transactions on Automatic Control,vol.53,11,pp.2658-2664,2008.
http://dx.doi.org/10.1109/TAC.2008.2007149
[16] S.Labiod,M.S.Boucherit, “Direct stable fuzzy adaptive control of a class of MIMO nonlinear systems”, Fuzzy sets and systems, vol.151,pp.59-77,2005.
http://dx.doi.org/10.1016/j.fss.2004.10.009
[17] N.Golea,A.Golea,K.benmahammed,“Stable indirect fuzzy adaptive control”,Fuzzy sets and systems,vol1.137,pp.353-366,2003.
http://dx.doi.org/10.1016/S0165-0114(02)00279-8
[18] Jinpeng Yu, Bing Chen, Haisheng Yu, “Position tracking control of induction motors via adaptive fuzzy backstepping” Energy Conversion and Management,vol51, pp.2345-2352,2010.
http://dx.doi.org/10.1016/j.enconman.2010.04.008
[19] F.L.Lewis,A.Yesildirek,K.Liu, “Multilayer neural net robot controller with guarantee tracking performance”,IEEE Transactions on Neural Networks,vol.7,pp.388-398,1996.
http://dx.doi.org/10.1109/72.485674
PMid:18255592
[20] Huang G B,Saratchandran, Sundararajan N. “A Generalized Growing and Pruning RBF (GGP-RBF) Neural Network for Function Approximation”.IEEE Transactions on Neural Networks,vol.16,pp.57-67,2005
http://dx.doi.org/10.1109/TNN.2004.836241
PMid:15732389
[21] J.-H.Park,G.-T.Park,S.-H.Kim,C.-J.Moon, “Direct adaptive self-structuring fuzzy controller for nonaffine nonlinear systems”, Fuzzy sets and systems, vol.153,pp.429-445,2005.
http://dx.doi.org/10.1016/j.fss.2005.01.003
[22] J.-H.Park, S.-H.Kim,C.-J.Moon, “Adaptive neural control for strict-feedback nonlinear systems without backstepping”,IEEE Transactions on Neural Networks, vol.20,7,pp.1204-1209,2009.
http://dx.doi.org/10.1109/TNN.2009.2020982
PMid:19482573
[23] H.-X,Li,S.C.Tong, “A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems”,IEEE Transactions on Fuzzy Systems,vol.11,pp.24-34,2003.
http://dx.doi.org/10.1109/TFUZZ.2002.806314
[24] G.Nurnberger, “Approximation by spline functions,”New York:Springer-Verlag,1999,
[25] J.T.Spooner,K.M.Passino, “Stable adaptive control using fuzzy systems and neural networks”,IEEE Transactions on Fuzzy Systems,vol.4,pp.339-359,1996.
http://dx.doi.org/10.1109/91.531775
Full Text: PDF