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Synchronization of fractional-order chaotic systems with Gaussian fluctuation by sliding mode control. (English) Zbl 1421.93135

Summary: Chaotic systems are always influenced by some uncertainties and external disturbances. This paper investigates the problem of practical synchronization of fractional-order chaotic systems with Gaussian fluctuation. A fractional integral (FI) sliding surface is proposed for synchronizing the uncertain fractional-order system, and then the sliding mode control technique is carried out to realize the synchronization of the given systems. One theorem about sliding mode controller is presented to prove that the proposed controller can make the system achieve synchronization. As a case study, the presented method is applied to the fractional-order Chen-Lü system, and simulation results show that the proposed control approach is capable to go against Gaussian noise well.

MSC:

93D99 Stability of control systems
34D06 Synchronization of solutions to ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93B12 Variable structure systems
93C15 Control/observation systems governed by ordinary differential equations
34A08 Fractional ordinary differential equations
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References:

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