Predictive control and synchronization of chaotic and hyperchaotic systems based on a T-S fuzzy model

This paper presents fuzzy model-based design for control and synchronization of chaotic systems. In this framework, the chaotic systems are exactly reproduced based on a Takagi-Sugeno (T-S) fuzzy model. Then the fuzzy controllers for control and synchronization are designed using the predictive method and some new and useful criteria are derived. Finally, numerical simulations are presented to illustrate the effectiveness and feasibility of the theoretical results.

[1]  O. Rössler The Chaotic Hierarchy , 1983 .

[2]  Noura Mansouri,et al.  Predictive Control of Continuous Chaotic Systems , 2008, Int. J. Bifurc. Chaos.

[3]  Kestutis Pyragas Continuous control of chaos by self-controlling feedback , 1992 .

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

[5]  O. Rössler An equation for hyperchaos , 1979 .

[6]  Xiaohong Zhang,et al.  Unified impulsive fuzzy-model-based controllers for chaotic systems with parameter uncertainties via LMI , 2010 .

[7]  X. Liao,et al.  Fuzzy modeling and synchronization of hyperchaotic systems , 2005 .

[8]  N. Mansouri,et al.  Fuzzy control of original UPOs of unknown discrete chaotic systems , 2012 .

[9]  Nikolay V. Kuznetsov,et al.  Hidden attractors in Dynamical Systems. From Hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman Problems to Hidden Chaotic Attractor in Chua Circuits , 2013, Int. J. Bifurc. Chaos.

[10]  Ruy Barboza Dynamics of a hyperchaotic Lorenz System , 2007, Int. J. Bifurc. Chaos.

[11]  ABDELKRIM BOUKABOU,et al.  Fuzzy Predictive Controller for Unknown Discrete Chaotic Systems , 2007, Int. J. Bifurc. Chaos.

[12]  Noura Mansouri,et al.  Control of n-scroll Chua's Circuit , 2009, Int. J. Bifurc. Chaos.

[13]  M. Bernardo An adaptive approach to the control and synchronization of continuous-time chaotic systems , 1996 .

[14]  E. Mosekilde,et al.  Chaotic hierarchy in a model of competing populations , 1993 .

[15]  Zhi-Hong Guan,et al.  LMI-based fuzzy stability and synchronization of Chen's system , 2003 .

[16]  Malek Benslama,et al.  Predictive synchronization of chaotic satellites systems , 2011, Expert Syst. Appl..

[17]  Zhidong Teng,et al.  General impulsive control of chaotic systems based on a TS fuzzy model , 2011, Fuzzy Sets Syst..

[18]  Kiyotaka Izumi,et al.  Fuzzy-chaos hybrid controller for controlling of nonlinear systems , 2002, IEEE Trans. Fuzzy Syst..

[19]  Abdelkrim Boukabou,et al.  Generalized chaos control and synchronization by nonlinear high-order approach , 2012, Math. Comput. Simul..

[20]  N. Inaba,et al.  OPF chaos control in a circuit containing a feedback voltage pulse generator , 1998 .

[21]  John L. Hudson,et al.  Higher chaos in a four-variable chemical reaction model , 1987 .

[22]  Noura Mansouri,et al.  Controlling Chaos in Higher-Order Dynamical Systems , 2004, Int. J. Bifurc. Chaos.

[23]  Zhi-Hong Guan,et al.  Impulsive synchronization for Takagi-Sugeno fuzzy model and its application to continuous chaotic system [rapid communication] , 2005 .

[24]  Daniel Franco,et al.  Global stabilization of fixed points using predictive control. , 2010, Chaos.

[25]  Noura Mansouri,et al.  T-S fuzzy control of uncertain chaotic vibration , 2012 .

[26]  Julien Clinton Sprott,et al.  Elementary quadratic chaotic flows with no equilibria , 2013 .

[27]  Nikolay V. Kuznetsov,et al.  Hidden attractor in smooth Chua systems , 2012 .

[28]  Toshimitsu Ushio,et al.  Stabilization of Unstable Periodic orbits of Chaotic Discrete-Time Systems Using Prediction-Based Feedback Control , 2002, Int. J. Bifurc. Chaos.

[29]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[30]  Xinzhi Liu,et al.  Impulsive stabilization and control of chaotic system , 2001 .

[31]  Toshimitsu Ushio,et al.  Prediction-based control of chaos , 1999 .

[32]  Kazuo Tanaka,et al.  A unified approach to controlling chaos via an LMI-based fuzzy control system design , 1998 .