Adaptive gain fuzzy sliding mode control for the synchronization of nonlinear chaotic gyros.

This paper proposes an adaptive gain fuzzy sliding mode control (AGFSMC) scheme for the synchronization of two nonlinear chaotic gyros in the presence of model uncertainties and external disturbances. In the AGFSMC scheme, the hitting controller that drives the system to the sliding surface is constructed by a set of fuzzy rules. In the proposed method, the gain of the reaching controller is adaptively adjusted to provide robustness against bounded uncertainties and external disturbances. The AGFSMC scheme can provide robustness in the absence of any knowledge about the bounds of uncertainties and external disturbances. We show that the adaptive gain scheme used in AGFSMC, improves the performance in comparison with the same control methodology that uses a fixed gain. Theoretical analysis of the AGFSMC scheme based on Lyapunov stability theory is provided. Numerical simulation on the application of the proposed method for the synchronization of two chaotic gyros is provided to demonstrate the feasibility of the method.

[1]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[2]  Jean-Jacques E. Slotine,et al.  The Robust Control of Robot Manipulators , 1985 .

[3]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[4]  Krauss.  Z decay and the search for dark matter. , 1990, Physical review letters.

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

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

[7]  Leon O. Chua,et al.  ON ADAPTIVE SYNCHRONIZATION AND CONTROL OF NONLINEAR DYNAMICAL SYSTEMS , 1996 .

[8]  J. Suykens,et al.  Robust nonlinear H/sub /spl infin// synchronization of chaotic Lur'e systems , 1997 .

[9]  V. Astakhov,et al.  Synchronization of chaotic oscillators by periodic parametric perturbations , 1997 .

[10]  T. Liao,et al.  Adaptive Synchronization of Two Lorenz Systemsfn1 , 1998 .

[11]  Guanrong Chen,et al.  From Chaos To Order Methodologies, Perspectives and Applications , 1998 .

[12]  Woonchul Ham,et al.  Adaptive fuzzy sliding mode control of nonlinear system , 1998, IEEE Trans. Fuzzy Syst..

[13]  Heinz G. Schuster,et al.  Handbook of Chaos Control: SCHUSTER:HDBK.CHAOS CONTR O-BK , 1999 .

[14]  Guanrong Chen,et al.  Switching manifold approach to chaos synchronization , 1999 .

[15]  Ahmad B. Rad,et al.  Indirect adaptive fuzzy sliding mode control: Part I: fuzzy switching , 2001, Fuzzy Sets Syst..

[16]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[17]  Jinhu Lu,et al.  Controlling Chen's chaotic attractor using backstepping design based on parameters identification , 2001 .

[18]  J. Sprott.  Chaos and time-series analysis , 2001 .

[19]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[20]  Yong Ren,et al.  Synchronization of discrete spatiotemporal chaos by using variable structure control , 2002 .

[21]  Kuang-Yow Lian,et al.  Adaptive synchronization design for chaotic systems via a scalar driving signal , 2002 .

[22]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

[23]  H.-K. Chen.  CHAOS AND CHAOS SYNCHRONIZATION OF A SYMMETRIC GYRO WITH LINEAR-PLUS-CUBIC DAMPING , 2002 .

[24]  S. Żak.  Systems and control , 2002 .

[25]  Chongzhao Han,et al.  Robust adaptive tracking control for a class of uncertain chaotic systems , 2003 .

[26]  Y. Xue,et al.  Synchronization of generalized Henon map by using adaptive fuzzy controller , 2003 .

[27]  Zhi-Hong Guan,et al.  Adaptive synchronization for Chen chaotic system with fully unknown parameters , 2004 .

[28]  Guanrong Chen,et al.  Adaptive control of discrete-time chaotic systems: a fuzzy control approach , 2004 .

[29]  Xiang-Jun Wu,et al.  Tracking control and synchronization of four-dimensional hyperchaotic Rossler system. , 2006, Chaos.

[30]  Jun-Juh Yan,et al.  Adaptive sliding mode control for synchronization of chaotic gyros with fully unknown parameters , 2006 .

[31]  M. Yassen.  Chaos control of chaotic dynamical systems using backstepping design , 2006 .

[32]  Chuandong Li,et al.  Synchronization of a class of coupled chaotic delayed systems with parameter mismatch. , 2007, Chaos.

[33]  Eckehard Schöll,et al.  Handbook of Chaos Control , 2007 .

[34]  M. Yassen.  Controlling, synchronization and tracking chaotic Liu system using active backstepping design , 2007 .

[35]  Kazuyuki Aihara,et al.  Impulsive control of stochastic systems with applications in chaos control, chaos synchronization, and neural networks. , 2008, Chaos.

[36]  M. Z. Jahromi,et al.  Synchronization of two different chaotic systems using novel adaptive fuzzy sliding mode control. , 2008, Chaos.

[37]  H. Salarieh,et al.  Adaptive synchronization of two different chaotic systems with time varying unknown parameters , 2008 .

[38]  M Roopaei,et al.  Synchronization of a class of chaotic systems with fully unknown parameters using adaptive sliding mode approach. , 2008, Chaos.

[39]  Wei Xu,et al.  Adaptive tracking control of a class of uncertain chaotic systems in the presence of random perturbations , 2008 .

[40]  Lotfi A. Zadeh,et al.  Is there a need for fuzzy logic? , 2008, NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society.

[41]  Her-Terng Yau,et al.  Chaos synchronization of two uncertain chaotic nonlinear gyros using fuzzy sliding mode control , 2008 .

[42]  Forced synchronization of a self-sustained chaotic oscillator. , 2008 .