Synchronization of the unified chaotic systems using a sliding mode controller

Abstract The unified chaotic system incorporates the behaviors of the Lorenz, the Chen and the Lu chaotic systems. This paper deals with the synchronization of two identical unified chaotic systems where the slave system is assumed to have a single input. A sliding mode controller is proposed to synchronize the two systems. The asymptotic convergence to zero of the errors between the states of the master and the slave systems is shown. Simulations results are presented to illustrate the proposed controller; they indicate that the designed controller is able to synchronize the unified chaotic systems. Also, simulation results show that the proposed control scheme is robust to random bounded disturbances acting on the master system. Moreover, the proposed scheme is applied to the secure communications field, where simulation results indicate that the proposed scheme is effective.

[1]  Zhiquan Wang,et al.  Generalized synchronization of unified chaotic system and the research of CSK , 2004, ICARCV.

[2]  A. Kanso,et al.  Logistic chaotic maps for binary numbers generations , 2009 .

[3]  Jun-an Lu,et al.  Synchronization of a unified chaotic system and the application in secure communication , 2002 .

[4]  Feng Hu,et al.  Two novel synchronization criterions for a unified chaotic system , 2006 .

[5]  Daizhan Cheng,et al.  Bridge the Gap between the Lorenz System and the Chen System , 2002, Int. J. Bifurc. Chaos.

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

[7]  Heng-Hui Chen,et al.  Adaptive synchronization of linearly coupled unified chaotic systems , 2009 .

[8]  Faqiang Wang,et al.  Synchronization of unified chaotic system based on passive control , 2007 .

[9]  Xiaoqun Wu,et al.  Linearly coupled synchronization of the unified chaotic systems and the Lorenz systems , 2005 .

[10]  Ju H. Park.  On synchronization of unified chaotic systems via nonlinear Control , 2005 .

[11]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[12]  Wei Zhang,et al.  Synchronization of unified chaotic systems with uncertain parameters based on the CLF , 2009 .

[13]  Jun-an Lu,et al.  Adaptive feedback synchronization of a unified chaotic system , 2004 .

[14]  J. Yan,et al.  Robust synchronization of unified chaotic systems via sliding mode control , 2007 .

[15]  M. Baptista.  Cryptography with chaos , 1998 .

[16]  Nejib Smaoui,et al.  Linear versus Nonlinear Dimensionality Reduction of High-Dimensional Dynamical Systems , 2004, SIAM J. Sci. Comput..

[17]  Junwei Wang,et al.  Designing synchronization schemes for chaotic fractional-order unified systems , 2006 .

[18]  Xiaofeng Liao,et al.  Impulsive control, complete and lag synchronization of unified chaotic system with continuous periodic switch , 2005 .

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

[20]  Xiaoming Deng,et al.  Secure communication based on synchronization of a unified chaotic system , 2004, Fifth World Congress on Intelligent Control and Automation (IEEE Cat. No.04EX788).

[21]  Swarup Poria,et al.  Synchronization of generalised linearly bidirectionally coupled unified chaotic system , 2009 .

[22]  Jianping Yan,et al.  Generalized projective synchronization of a unified chaotic system , 2005 .

[23]  Shihua Chen,et al.  Impulsive control and synchronization of unified chaotic system , 2004 .

[24]  Er-Wei Bai,et al.  Synchronization of the unified chaotic systems via active control , 2006 .

[25]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[26]  S. Čelikovský,et al.  Control systems: from linear analysis to synthesis of chaos , 1996 .

[27]  Wu Xiaoqun,et al.  Control of a unified chaotic system with delayed continuous periodic switch , 2004 .

[28]  Guanrong Chen,et al.  Bifurcation control of two nonlinear models of cardiac activity , 1997 .

[29]  Liang Feng,et al.  Projective Synchronization and Control of Unified Chaotic System , 2005 .

[30]  Ju H. Park.  Adaptive modified projective synchronization of a unified chaotic system with an uncertain parameter , 2007 .

[31]  Yongguang Yu.  Adaptive synchronization of a unified chaotic system , 2008 .

[32]  Jie Liu,et al.  Parameter identification and control of uncertain unified chaotic system via adaptive extending equilibrium manifold approach , 2004 .

[33]  Guanrong Chen,et al.  Controlling a unified chaotic system to hyperchaotic , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[34]  Ricardo Femat,et al.  Adaptive synchronization of high-order chaotic systems: a feedback with low-order parametrization , 2000 .

[35]  Xing-yuan Wang,et al.  Synchronization of the unified chaotic system , 2008 .

[36]  Rolf Dieter Schraft,et al.  Automation and Robotics , 2007 .

[37]  F. M. Moukam Kakmeni,et al.  Synchronizing chaotic dynamics with uncertainties using a predictable synchronization delay design , 2006 .