Adaptive CMAC neural control of chaotic systems with a PI-type learning algorithm

The cerebellar model articulation controller (CMAC) has the advantages such as fast learning property, good generalization capability and information storing ability. Based on these advantages, this paper proposes an adaptive CMAC neural control (ACNC) system with a PI-type learning algorithm and applies it to control the chaotic systems. The ACNC system is composed of an adaptive CMAC and a compensation controller. Adaptive CMAC is used to mimic an ideal controller and the compensation controller is designed to dispel the approximation error between adaptive CMAC and ideal controller. Based on the Lyapunov stability theorems, the designed ACNC feedback control system is guaranteed to be uniformly ultimately bounded. Finally, the ACNC system is applied to control two chaotic systems, a Genesio chaotic system and a Duffing-Holmes chaotic system. Simulation results verify that the proposed ACNC system with a PI-type learning algorithm can achieve better control performance than other control methods.

[1]  Chih-Min Lin,et al.  Adaptive CMAC-based supervisory control for uncertain nonlinear systems , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[2]  Chun-Fei Hsu,et al.  Self-Organizing Adaptive Fuzzy Neural Control for a Class of Nonlinear Systems , 2007, IEEE Transactions on Neural Networks.

[3]  Chih-Min Lin,et al.  Missile guidance law design using adaptive cerebellar model articulation controller , 2005, IEEE Transactions on Neural Networks.

[4]  Guanrong Chen,et al.  On feedback control of chaotic continuous-time systems , 1993 .

[5]  Amar Goléa,et al.  Fuzzy model reference adaptive control , 2002, IEEE Trans. Fuzzy Syst..

[6]  J. Yan,et al.  Adaptive variable structure control for uncertain chaotic systems containing dead-zone nonlinearity☆ , 2005 .

[7]  Antonio Loría,et al.  Adaptive Tracking Control of Chaotic Systems With Applications to Synchronization , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[8]  Chun-Fei Hsu.  Design of intelligent power controller for DC–DC converters using CMAC neural network , 2007, Neural Computing and Applications.

[9]  Louis M. Pecora,et al.  Synchronizing chaotic circuits , 1991 .

[10]  F. Chang,et al.  Adaptive fuzzy CMAC control for a class of nonlinear systems with smooth compensation , 2006 .

[11]  David L. Elliott,et al.  Neural Systems for Control , 1997 .

[12]  Oguz Ustun,et al.  A neuro-fuzzy controller for speed control of a permanent magnet synchronous motor drive , 2008, Expert Syst. Appl..

[13]  Shun-Feng Su,et al.  Credit assigned CMAC and its application to online learning robust controllers , 2003, IEEE Trans. Syst. Man Cybern. Part B.

[14]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[15]  Shih-Lin Hung,et al.  High-order MS CMAC neural network , 2001, IEEE Trans. Neural Networks.

[16]  Her-Terng Yau,et al.  Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems , 2006 .

[17]  Chih-Min Lin,et al.  Neural-network hybrid control for antilock braking systems , 2003, IEEE Trans. Neural Networks.

[18]  Chih-Min Lin,et al.  Wavelet Adaptive Backstepping Control for a Class of Nonlinear Systems , 2006, IEEE Transactions on Neural Networks.

[19]  Michael Peter Kennedy,et al.  The role of synchronization in digital communications using chaos. II. Chaotic modulation and chaotic synchronization , 1998 .

[20]  Yih-Guang Leu,et al.  Observer-based direct adaptive fuzzy-neural control for nonaffine nonlinear systems , 2005, IEEE Trans. Neural Networks.

[21]  Chih-Min Lin,et al.  Supervisory recurrent fuzzy neural network control of wing rock for slender delta wings , 2004, IEEE Trans. Fuzzy Syst..

[22]  Cong Wang,et al.  Learning from neural control , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[23]  Bin Deng,et al.  Observer-based robust adaptive variable universe fuzzy control for chaotic system , 2005 .

[24]  Jang-Hyun Park,et al.  Robust adaptive fuzzy controller for nonlinear system using estimation of bounds for approximation errors , 2003, Fuzzy Sets Syst..