Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller. (English) Zbl 1248.93146

Aghababa, Mohammad Pourmahmood

Commun. Nonlinear Sci. Numer. Simul. 17, No. 6, 2670-2681 (2012).

Summary: This paper proposes a novel fractional-order sliding mode approach for stabilization and synchronization of a class of fractional-order chaotic systems. Based on the fractional calculus, a stable integral type fractional-order sliding surface is introduced. Using the fractional Lyapunov stability theorem, a single sliding mode control law is proposed to ensure the existence of the sliding motion in finite time. The proposed control scheme is applied to stabilize/synchronize a class of fractional-order chaotic systems in the presence of model uncertainties and external disturbances. Some numerical simulations are performed to confirm the theoretical results of the paper. It is worth to emphasize that the proposed fractional-order sliding mode controller can be applied to control a broad range of fractional-order dynamical systems.

MSC:

93D21	Adaptive or robust stabilization
93C15	Control/observation systems governed by ordinary differential equations
34D06	Synchronization of solutions to ordinary differential equations
37N35	Dynamical systems in control
93B12	Variable structure systems

Keywords:

chaotic system; fractional-order sliding surface; finite time reaching phase; stabilization; synchronization

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