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Sliding mode synchronization of an uncertain fractional order chaotic system. (English) Zbl 1189.34011

Summary: 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.

MSC:

34A08 Fractional ordinary differential equations
26A33 Fractional derivatives and integrals
93B52 Feedback control
37N35 Dynamical systems in control
34D06 Synchronization of solutions to ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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