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Adaptive impulsive synchronization of uncertain chaotic systems. (English) Zbl 1237.34099

Summary: The Letter develops an adaptive impulsive scheme that includes a sole restriction criterion to achieve synchronization of chaotic nonlinear systems with unknown parameters. The system is assumed to satisfy the local Lipschitz condition while a Lipschitz constant and the uncertain system parameters are estimated by augmented adaptation equations. Adaptation of all parameters is proven to converge exponentially. The significance of the related control parameters and their margins in the criterion is also discussed in detail. The Lorenz system has been simulated to illustrate the theoretical analysis.

MSC:

34D06 Synchronization of solutions to ordinary differential equations
34H10 Chaos control for problems involving ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
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