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Wang, Zengyun; Huang, Lihong; Yang, Xuxin; Lu, Dingyang

Adaptive synchronization for two different stochastic chaotic systems with unknown parameters via a sliding mode controller. (English) Zbl 1291.93087

Abstr. Appl. Anal. 2013, Article ID 452549, 12 p. (2013).
Summary: This paper investigates the problem of synchronization for two different stochastic chaotic systems with unknown parameters and uncertain terms. The main work of this paper consists of the following aspects. Firstly, based on the Lyapunov theory in stochastic differential equations and the theory of sliding mode control, we propose a simple sliding surface and discuss the occurrence of the sliding motion. Secondly, we design an adaptive sliding mode controller to realize the asymptotical synchronization in mean squares. Thirdly, we design an adaptive sliding mode controller to realize the almost surely synchronization. Finally, the designed adaptive sliding mode controllers are used to achieve synchronization between two pairs of different stochastic chaos systems (Lorenz-Chen and Chen-Lu) in the presence of the uncertainties and unknown parameters. Numerical simulations are given to demonstrate the robustness and efficiency of the proposed robust adaptive sliding mode controller.

MSC:

93B12 Variable structure systems
93E03 Stochastic systems in control theory (general)
34D06 Synchronization of solutions to ordinary differential equations
34H10 Chaos control for problems involving ordinary differential equations
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