Sliding mode controller design for chaos synchronization of Rikitake chaotic systems

In this paper, synchronization of Rikitake chaotic systems and its application in secure communication are presented. Sliding mode control is using scheme to solve the synchronization problem of Rikitake chaotic systems. The proposed scheme guarantees the synchronization between the master and slave Rikitake chaotic systems based on the use of Lyapunov stability theory. Moreover, the selection of switching surface and the existence of sliding mode is addressed. Finally, the experimental results validate the proposed chaotic synchronization approach.

[1]  Ju H. Park.  Adaptive Synchronization of a Unified Chaotic System with an Uncertain Parameter , 2005 .

[2]  Pei Yu,et al.  Chaos control for the family of Rössler systems using feedback controllers , 2006 .

[3]  Hsin-Chieh Chen,et al.  Synchronization of Unified Chaotic Systems Using Sliding Mode Controller , 2012 .

[4]  Peter Liu,et al.  Synthesis of fuzzy model-based designs to synchronization and secure communications for chaotic systems , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[5]  José Manoel Balthazar,et al.  On an optimal control design for Rössler system , 2004 .

[6]  Yaghoub Heidari,et al.  Adaptive Robust Pid Controller Design Based On A Sliding Mode For Uncertain Chaotic Systems , 2012 .

[7]  Teh-Lu Liao,et al.  An observer-based approach for chaotic synchronization with applications to secure communications , 1999 .

[8]  H. Agiza,et al.  Controlling and Synchronization of Rossler System with Uncertain Parameters , 2004 .

[9]  Ivan Zelinka,et al.  Chaos synchronization of unknown inputs Takagi-Sugeno fuzzy: Application to secure communications , 2014, Comput. Math. Appl..

[10]  Ming-Jyi Jang,et al.  Sliding Mode Control of Chaos in the cubic Chua's Circuit System , 2002, Int. J. Bifurc. Chaos.

[11]  Peter Liu,et al.  Secure communications of chaotic systems with robust performance via fuzzy observer-based design , 2001, IEEE Trans. Fuzzy Syst..

[12]  T. Rikitake,et al.  Oscillations of a system of disk dynamos , 1958, Mathematical Proceedings of the Cambridge Philosophical Society.

[13]  Vadim I. Utkin,et al.  Sliding Modes and their Application in Variable Structure Systems , 1978 .

[14]  H. N. Agiza,et al.  Chaos synchronization of Lü dynamical system , 2004 .

[15]  Weigao Ge,et al.  Periodic solution and chaotic strange attractor for shunting inhibitory cellular neural networks with impulses. , 2006, Chaos.

[16]  Jitao Sun,et al.  Impulsive control and synchronization of Chua's oscillators , 2004, Math. Comput. Simul..

[17]  Haizhen He,et al.  Time-controllable combinatorial inner synchronization and outer synchronization of anti-star networks and its application in secure communication , 2015, Commun. Nonlinear Sci. Numer. Simul..

[18]  Mahmood Mola,et al.  Investigation stability of Rikitake system , 2014 .