Finite-Time Adaptive Synchronization of a New Hyperchaotic System with Uncertain Parameters

This paper presents a finite-time adaptive synchronization strategy for a class of new hyperchaotic systems with unknown slave system’s parameters. Based on the finite-time stability theory, an adaptive control law is derived to make the states of the new hyperchaotic systems synchronized in finite-time. Numerical simulations are presented to show the effectiveness of the proposed finite time synchronization scheme.

[1]  S. S. Yang,et al.  Generalized Synchronization in Chaotic Systems , 1998 .

[2]  J. M. González-Miranda,et al.  Synchronization of Chaotic Oscillators , 2011 .

[3]  Jiang-Wen Xiao,et al.  Impulsive control for synchronization of a class of continuous systems. , 2004, Chaos.

[4]  Grigory V. Osipov,et al.  PHASE SYNCHRONIZATION EFFECTS IN A LATTICE OF NONIDENTICAL ROSSLER OSCILLATORS , 1997 .

[5]  S. Bishop,et al.  Manipulating the scaling factor of projective synchronization in three-dimensional chaotic systems. , 2001, Chaos.

[6]  Wuquan Li,et al.  Finite-time generalized synchronization of chaotic systems with different order , 2011 .

[7]  José Manoel Balthazar,et al.  On control and synchronization in chaotic and hyperchaotic systems via linear feedback control , 2008 .

[8]  Zhenya Yan,et al.  Q-S (lag or anticipated) synchronization backstepping scheme in a class of continuous-time hyperchaotic systems--a symbolic-numeric computation approach. , 2005, Chaos.

[9]  Baocang Ding,et al.  A synthesis approach for output feedback robust constrained model predictive control , 2008, Autom..

[10]  Giuseppe Grassi,et al.  New 3D-scroll attractors in hyperchaotic Chua's Circuits Forming a Ring , 2003, Int. J. Bifurc. Chaos.

[11]  Longge Zhang,et al.  Robust synchronization of two different uncertain fractional-order chaotic systems via adaptive sliding mode control , 2014 .

[12]  Yang Ying,et al.  Finite time control of a class of time-varying unified chaotic systems. , 2013, Chaos.

[13]  M. P. Aghababa,et al.  A general nonlinear adaptive control scheme for finite-time synchronization of chaotic systems with uncertain parameters and nonlinear inputs , 2012 .

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

[15]  Ronnie Mainieri,et al.  Projective Synchronization In Three-Dimensional Chaotic Systems , 1999 .

[16]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  Liu Xiangjie,et al.  The synchronization between two discrete-time chaotic systems using active robust model predictive control , 2013 .

[18]  Wenguang Yu.  Finite-time stabilization of three-dimensional chaotic systems based on CLF , 2010 .

[19]  J. Kurths,et al.  From Phase to Lag Synchronization in Coupled Chaotic Oscillators , 1997 .

[20]  Faqiang Wang,et al.  A new criterion for chaos and hyperchaos synchronization using linear feedback control , 2006 .

[21]  Xiaofeng Liao,et al.  Lag synchronization of Rossler system and Chua circuit via a scalar signal , 2004 .

[22]  Tingwen Huang,et al.  Anticipating synchronization of a class of chaotic systems. , 2009, Chaos.

[23]  Guanrong Chen,et al.  Chaos quasisynchronization induced by impulses with parameter mismatches. , 2006, Chaos.

[24]  Guanrong Chen,et al.  Generating Hyperchaos via State Feedback Control , 2005, Int. J. Bifurc. Chaos.

[25]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[26]  Biao Huang,et al.  Reformulation of LMI-based stabilisation conditions for non-linear systems in Takagi–Sugeno's form , 2008, Int. J. Syst. Sci..

[27]  H. Agiza,et al.  Synchronization of Rossler and Chen chaotic dynamical systems using active control , 2001, Physics Letters A.

[28]  Tingwen Huang,et al.  Impulsive stabilization and synchronization of a class of chaotic delay systems. , 2005, Chaos.

[29]  Xiaofeng Liao,et al.  Complete and lag synchronization of hyperchaotic systems using small impulses , 2004 .

[30]  Tao Yang,et al.  Synchronizing chaotic dynamics with uncertainties based on a sliding mode control design. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Yugeng Xi,et al.  Improving off-line approach to robust MPC based-on nominal performance cost , 2007, Autom..

[32]  M. P. Aghababa.  Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique , 2012 .

[33]  Yongjian Liu,et al.  Circuit implementation and finite-time synchronization of the 4D Rabinovich hyperchaotic system , 2011, Nonlinear Dynamics.

[34]  Ningning Yang,et al.  A novel fractional-order hyperchaotic system stabilization via fractional sliding-mode control , 2013 .

[35]  Zuolei Wang,et al.  Anti-synchronization in two non-identical hyperchaotic systems with known or unknown parameters , 2009 .

[36]  Jinhu Lu,et al.  Synchronization of an uncertain unified chaotic system via adaptive control , 2002 .

[37]  Wei Zhang,et al.  Finite-time chaos synchronization of unified chaotic system with uncertain parameters , 2009 .

[38]  Young-Jai Park,et al.  Anti-synchronization of chaotic oscillators , 2003 .

[39]  U. Vincent,et al.  Finite-time synchronization for a class of chaotic and hyperchaotic systems via adaptive feedback controller , 2011 .

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

[41]  Sara Dadras,et al.  Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form , 2012 .