Two fuzzy control schemes for Lorenz-Stenflo chaotic system

In this paper, two effective fuzzy control schemes, i.e., fuzzy feedback control method and adaptive fuzzy control method are introduced to suppress the state variables of the Lorenz-Stenflo chaotic system (LSCS) to its equilibrium point. For the first fuzzy control scheme, with the abundant modeling capability of the T-S fuzzy model, the LSCS can be decomposed into some local linear systems, which makes it very convenient to use the fuzzy feedback control method to analyze it. Based on the Lyapunov stability theorem, a criterion is also derived to guarantee the controlled LSCS is robust stable at the equilibrium point, even if there exist external perturbations. For the second fuzzy control scheme, fuzzy logic systems areexploited to approximate the nonlinear functions. Moreover, an adaptive technique is employed to construct an effective fuzzy controller, which can drive all state variables into a rather small neighborhood of its equilibrium point. By choosing a group of suitable parameters, the controlled system can approach the equilibrium point with high precision. Two numerical simulations are presented to demonstrate the effectiveness and feasibility of the two fuzzy control schemes.

[1]  P.M.J. Van den Hof,et al.  Bang-bang control and singular arcs in reservoir flooding , 2007 .

[2]  Shih-Yu Li,et al.  Chaos control of new Mathieu-Van der Pol systems with new Mathieu-Duffing systems as functional system by GYC partial region stability theory , 2009 .

[3]  Pramod P. Khargonekar,et al.  H 2 optimal control for sampled-data systems , 1991 .

[4]  T. Liao,et al.  Controlling chaos of the family of Rossler systems using sliding mode control , 2008 .

[5]  Changchun Hua,et al.  Adaptive feedback control for a class of chaotic systems , 2005 .

[6]  Sahjendra N. Singh,et al.  Adaptive Control of Chaos in Lorenz System , 1997 .

[7]  Santo Banerjee,et al.  Chaos, signal communication and parameter estimation , 2004 .

[8]  Choy Heng Lai,et al.  Secured Encryption using Chaotic Carriers , 1999 .

[9]  Pramod P. Khargonekar,et al.  Synthesis of H/sub 2/ optimal controllers for sampled-data systems , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[10]  L. Stenflo,et al.  Nonlinear acoustic-gravity waves , 2009 .

[11]  Moez Feki,et al.  An adaptive feedback control of linearizable chaotic systems , 2003 .

[12]  S. Tong,et al.  Adaptive fuzzy approach to control unified chaotic systems , 2007 .

[13]  Shinji Hara,et al.  Feedback linearization for pneumatic actuator systems with static friction , 1997 .

[14]  F.H.F. Leung,et al.  A chattering elimination algorithm for sliding mode control of uncertain non-linear systems , 1998 .

[15]  Edward Ott,et al.  Controlling chaos , 2006, Scholarpedia.

[16]  J. Wen,et al.  Adaptive fuzzy control for a class of chaotic systems with nonaffine inputs , 2011 .

[17]  Tingwen Huang,et al.  Impulsive synchronization and parameter mismatch of the three-variable autocatalator model , 2007 .

[18]  L. Yang,et al.  Impulsive control for synchronization of nonlinear Rössler chaotic systems , 2006 .

[19]  A. Roy Chowdhury,et al.  On the application of adaptive control and phase synchronization in non-linear fluid dynamics , 2004 .

[20]  Uri Shaked,et al.  Robust Hinfinity output-feedback control of systems with time-delay , 2008, Syst. Control. Lett..

[21]  李晓辉,et al.  LMI-based output feedback fuzzy control of chaotic system with uncertainties * , 2006 .

[22]  Tung,et al.  Controlling chaos using differential geometric method. , 1995, Physical review letters.

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

[24]  Xin-Ping Guan,et al.  Adaptive fuzzy control for chaotic systems with H[infin] tracking performance , 2003, Fuzzy Sets Syst..