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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 452549, 12 pages
http://dx.doi.org/10.1155/2013/452549
Research Article

Adaptive Synchronization for Two Different Stochastic Chaotic Systems with Unknown Parameters via a Sliding Mode Controller

1Department of Mathematics, Hunan First Normal University, Changsha 410205, China
2College of Mathematics and Econometrics, Hunan University, Changsha 410082, China
3Hunan Women's University, Changsha 410003, China

Received 31 January 2013; Accepted 19 March 2013

Academic Editor: René Yamapi

Copyright © 2013 Zengyun Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.