Synchronization of a class of chaotic systems with fully unknown parameters using adaptive sliding mode approach.

In this paper, an adaptive sliding mode control method for synchronization of a class of chaotic systems with fully unknown parameters is introduced. In this method, no knowledge of the bounds of parameters is required in advance and the parameters are updated through an adaptive control process. We use our proposed method to synchronize two chaotic gyros, which has been the subject of intense study during the recent years for its application in the navigational, aeronautical, and space engineering domains. The effectiveness of our method is demonstrated in simulation environment and the results are compared with some recent schemes proposed in the literature for the same task.

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

[2]  Di Zhou,et al.  Adaptive Nonlinear Synchronization Control of Twin-Gyro Precession , 2006 .

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

[4]  R. Leipnik,et al.  Double strange attractors in rigid body motion with linear feedback control , 1981 .

[5]  Z. Ge,et al.  THE REGULAR AND CHAOTIC MOTIONS OF A SYMMETRIC HEAVY GYROSCOPE WITH HARMONIC EXCITATION , 1996 .

[6]  Z. Ge,et al.  Bifurcations and chaos in a rate gyro with harmonic excitation , 1996 .

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

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

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

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

[11]  X. Tong,et al.  Chaotic Motion of a Symmetric Gyro Subjected to a Harmonic Base Excitation , 2001 .

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

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

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

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

[16]  Wei Xu,et al.  Synchronization of two chaotic nonlinear gyros using active control , 2005 .

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

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

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

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

[21]  R. V. Dooren,et al.  Comments on “Chaos and chaos synchronization of a symmetric gyro with linear-plus-cubic damping” , 2003 .

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

[23]  Leon O. Chua,et al.  ADAPTIVE SYNCHRONIZATION OF CHUA'S OSCILLATORS , 1996 .

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

[25]  H.-K. Chen,et al.  Synchronization of chaotic symmetric gyros by one-way coupling conditions , 2003 .

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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