Nonlinear Dynamics

, Volume 66, Issue 1–2, pp 89–97 | Cite as

Chaos synchronization for a class of nonequivalent systems with restrictive inputs via time-varying sliding mode

Original Paper


In this paper, the synchronization between Duffing and Van der Pol chaotic systems with control inputs constraint is investigated. In practice, the maximum admissible values of the control inputs are restrained. To solve this problem, based on time-varying sliding mode theory, we can obtain the best possible control quality without violating technical and environmental constraints by selecting the switching line parameters. Also a kind of extended state observer is used to compensate for the uncertainties of systems, using only the available synchronizing error. Then the controller becomes physically realizable based on the states of the observer, and can be used to synchronize between Duffing and Van der Pol chaotic systems. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control scheme.


Chaos synchronization Time-varying sliding mode Maximum admissible control input Extended state observer 


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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Artificial Intelligence Key Laboratory of Sichuan ProvinceSichuan University of Science and EngineeringZigongChina
  2. 2.Faculty of Electronic Information and Electrical EngineeringDalian University of TechnologyDalianChina

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