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Mathematical Problems in Engineering
Volume 2013, Article ID 859304, 5 pages
http://dx.doi.org/10.1155/2013/859304
Research Article

Parameter Identification and Synchronization of Uncertain Chaotic Systems Based on Sliding Mode Observer

Harbin Engineering University, Harbin, Heilongjiang 150001, China

Received 25 July 2013; Accepted 6 September 2013

Academic Editor: Guanghui Sun

Copyright © 2013 Li-lian Huang and Lei Lin. 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

The synchronization of nonlinear uncertain chaotic systems is investigated. We propose a sliding mode state observer scheme which combines the sliding mode control with observer theory and apply it into the uncertain chaotic system with unknown parameters and bounded interference. Based on Lyapunov stability theory, the constraints of synchronization and proof are given. This method not only can realize the synchronization of chaotic systems, but also identify the unknown parameters and obtain the correct parameter estimation. Otherwise, the synchronization of chaotic systems with unknown parameters and bounded external disturbances is robust by the design of the sliding surface. Finally, numerical simulations on Liu chaotic system with unknown parameters and disturbances are carried out. Simulation results show that this synchronization and parameter identification has been totally achieved and the effectiveness is verified very well.