Sliding mode synchronization of an uncertain fractional order chaotic system

Synchronization of chaotic and uncertain Duffing-Holmes system has been done using the sliding mode control strategy. Regarding the synchronization task as a control problem, fractional order mathematics is used to express the system and sliding mode for synchronization. It has been shown that, not only the performance of the proposed method is satisfying with an acceptable level of control signal, but also a rather simple stability analysis is performed. The latter is usually a complicated task for uncertain nonlinear chaotic systems.

[1]  Yuan Kang,et al.  Chaos in the Newton–Leipnik system with fractional order , 2008 .

[2]  Junguo Lu.  Chaotic dynamics of the fractional-order Lü system and its synchronization , 2006 .

[3]  D. Matignon.  Stability results for fractional differential equations with applications to control processing , 1996 .

[4]  I. Podlubny.  Fractional differential equations , 1998 .

[5]  Guanrong Chen,et al.  A note on the fractional-order Chen system , 2006 .

[6]  Chunguang Li,et al.  Chaos and hyperchaos in the fractional-order Rössler equations , 2004 .

[7]  Edward Ott,et al.  Controlling chaos , 2006, Scholarpedia.

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

[9]  Jun-Guo Lu,et al.  Chaotic dynamics and synchronization of fractional-order Arneodo’s systems , 2005 .

[10]  Tao Yang,et al.  A SURVEY OF CHAOTIC SECURE COMMUNICATION SYSTEMS , 2004 .

[11]  Jianming Lu,et al.  Chattering Free Sliding Mode Control in Magnetic Levitation System , 2005 .

[12]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[13]  J. J. Slotine,et al.  Tracking control of non-linear systems using sliding surfaces with application to robot manipulators , 1983, 1983 American Control Conference.

[14]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[15]  C. F. Lorenzo,et al.  Chaos in a fractional order Chua's system , 1995 .

[16]  E. Ahmed,et al.  Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models , 2007 .

[17]  Julien Clinton Sprott,et al.  Chaos in fractional-order autonomous nonlinear systems , 2003 .

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

[19]  Okyay Kaynak,et al.  Neuro-sliding mode control of robotic manipulators , 1997, 1997 8th International Conference on Advanced Robotics. Proceedings. ICAR'97.

[20]  W. Deng,et al.  Chaos synchronization of the fractional Lü system , 2005 .