Uncertain Fractional Order Chaotic Systems Tracking Design via Adaptive Hybrid Fuzzy Sliding Mode Control

In this paper, in order to achieve tracking performance of uncertain fractional order chaotic systems an adaptive hybrid fuzzy controller is proposed. During the design procedure, a hybrid learning algorithm combining sliding mode control and Lyapunov stability criterion is adopted to tune the free parameters on line by output feedback control law and adaptive law. A weighting factor, which can be adjusted by the trade-off between plant knowledge and control knowledge, is adopted to sum together the control efforts from indirect adaptive fuzzy controller and direct adaptive fuzzy controller. To confirm effectiveness of the proposed control scheme, the fractional order chaotic response system is fully illustrated to track the trajectory generated from the fractional order chaotic drive system. The numerical results show that tracking error and control effort can be made smaller and the proposed hybrid intelligent control structure is more flexible during the design process.

[1]  Ivo Petras,et al.  A note on the fractional-order Chua’s system , 2008 .

[2]  M. Haeri,et al.  Synchronization of chaotic fractional-order systems via active sliding mode controller , 2008 .

[3]  M.M. Balas,et al.  World Knowledge for Control Applications , 2007, 2007 11th International Conference on Intelligent Engineering Systems.

[4]  Lotfi A. Zadeh,et al.  Fuzzy logic, neural networks, and soft computing , 1993, CACM.

[5]  Li-Xin Wang,et al.  Adaptive fuzzy systems and control - design and stability analysis , 1994 .

[6]  Lotfi A. Zadeh,et al.  Knowledge Representation in Fuzzy Logic , 1996, IEEE Trans. Knowl. Data Eng..

[7]  Reza Ghaderi,et al.  Sliding mode synchronization of an uncertain fractional order chaotic system , 2010, Comput. Math. Appl..

[8]  K. Diethelm AN ALGORITHM FOR THE NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER , 1997 .

[9]  Tsung-Chih Lin,et al.  Adaptive hybrid intelligent control for uncertain nonlinear dynamical systems , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[10]  M. MendelJ.,et al.  Fuzzy basis functions , 1995 .

[11]  L. A. Zedeh Knowledge representation in fuzzy logic , 1989 .

[12]  L X Wang,et al.  Fuzzy basis functions, universal approximation, and orthogonal least-squares learning , 1992, IEEE Trans. Neural Networks.

[13]  Guanrong Chen,et al.  A note on the fractional-order Chen system , 2006 .

[14]  Tsung-Chih Lin,et al.  Direct adaptive fuzzy-neural control with state observer and supervisory controller for unknown nonlinear dynamical systems , 2002, IEEE Trans. Fuzzy Syst..

[15]  Ivo Petrás,et al.  A Note on the Fractional-Order Cellular Neural Networks , 2006, The 2006 IEEE International Joint Conference on Neural Network Proceedings.

[16]  Tsung-Chih Lin,et al.  Observer-based indirect adaptive fuzzy-neural tracking control for nonlinear SISO systems using VSS and H[infin] approaches , 2004, Fuzzy Sets Syst..

[17]  Shuzhi Sam Ge,et al.  Adaptive Neural Network Control of Robotic Manipulators , 1999, World Scientific Series in Robotics and Intelligent Systems.

[18]  Juan Luis Castro,et al.  Fuzzy logic controllers are universal approximators , 1995, IEEE Trans. Syst. Man Cybern..

[19]  X. Yuan,et al.  Robust TS Fuzzy Design for Uncertain Nonlinear Systems with State Delays Based on Sliding Mode Control , 2010 .

[20]  Yaonan Wang,et al.  H∞ Robust T-S Fuzzy Design for Uncertain Nonlinear Systems with State Delays Based on Sliding Mode Control , 2010, Int. J. Comput. Commun. Control.

[21]  Lotfi A. Zadeh,et al.  Fuzzy Logic , 2009, Encyclopedia of Complexity and Systems Science.

[22]  Juebang Yu,et al.  Chaos in the fractional order periodically forced complex Duffing’s oscillators , 2005 .

[23]  P. Arena,et al.  Bifurcation and Chaos in Noninteger Order Cellular Neural Networks , 1998 .

[24]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .