This note further investigates the locally and globally adaptive synchronization of an uncertain complex dynamical network. Several network synchronization criteria are deduced. Especially, our hypotheses and designed adaptive controllers for network synchronization are rather simple in form. It is very useful for future practical engineering design. Moreover, numerical simulations are also given to show the effectiveness of our synchronization approaches.

Adaptive synchronization of an uncertain complex dynamical network

Backstepping design is proposed for synchronization of Genesio chaotic system. Firstly, the control problem for the chaos synchronization of nominal Genesio systems without unknown parameters is considered. Next, an adaptive backstepping control law is derived to make the error signals between drive Genesio system and response Genesio system with an uncertain parameter asymptotically synchronized. Finally, the approach is extended to the synchronization problem for the system with three unknown parameters. The stability analysis in this article is proved by using a well-known Lyapunov stability theorem. Note that the approach provided here needs only a single controller to realize the synchronization. Two numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.

Synchronization of Genesio chaotic system via backstepping approach

Analysis, control, synchronization, and circuit design of a novel chaotic system

s: Monsees, G. and J. M. A. Scherpen (2001), “Discrete-time output-based sliding mode control”, Proceedings of the 20th Benelux Meeting on Systems and Control, Houfalize, Belgium. Monsees, G., K. George, J. M. A. Scherpen and M. Verhaegen (1999), “A feedforward-feedback interpretation of a sliding mode control law”, Proceedings of the 18th Benelux Meeting on Systems and Control, Houthalen, Belgium.

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Discrete-time sliding mode control

Adaptive synchronization between two different chaotic systems with unknown parameters

Adaptive feedback synchronization of a unified chaotic system

This letter further improves and extends the works of Chen and Lu [Chaos, Solitons & Fractals 14 (2002) 643] and Wang et al. [Phys. Lett. A 312 (2003) 34]. In detail, the linear feedback synchronization and adaptive feedback synchronization for Lu system are discussed. And the lower bound of the feedback gain in linear feedback synchronization is presented. The adaptive feedback synchronization with only one controller is designed, which improves the proof in the work by Wang et al. The adaptive synchronization with two controllers for completely uncertain Lu system is also discussed, which extends the work of Chen and Lu. Also, numerical simulations show the effectiveness of these methods.

Adaptive feedback synchronization of Lü system

In the past years, impulsive control for a single system and impulsive synchronization between two systems have been extensively studied. However, investigation on impulsive control and synchronization of complex networks has just started. In these studies, a network is continuously coupled, and then is synchronized by using impulsive control strategy. In this paper, a new and different coupled model is proposed, where the systems are coupled only at discrete instants through impulsive connections. Several criteria for synchronizing such kind of impulsively coupled complex dynamical systems are established. Two examples are also worked through for illustrating the main results.

Synchronization of impulsively coupled systems

Leader-following synchronization of coupled time-delay neural networks via delayed impulsive control

This paper is concerned with the problem of the robust stability of fractional-order memristive bidirectional associative memory (BAM) neural networks. Based on Lyapunov theory, fractional-order differential inequalities and linear matrix inequalities (LMI) are applied to obtain a robust asymptotical stability. Finally, numerical examples are presented.

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Xiuping Han

Papers

Adaptive feedback synchronization of a unified chaotic system

Adaptive feedback synchronization of Lü system

Synchronization of impulsively coupled systems

Leader-following synchronization of coupled time-delay neural networks via delayed impulsive control

Robust Stability of Fractional Order Memristive BAM Neural Networks with Mixed and Additive Time Varying Delays