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02/2011; , ISBN: 978-953-307-564-8
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ABSTRACT: In this paper a nonlinear control method based on Lyapunov stability theorem is proposed to design an adaptive controller for synchronizing two different chaotic systems. It is assumed that the unknown parameters of the drive and the response chaotic systems are time varying. It is shown that the proposed scheme can identify the system parameters if the system parameters are time invariant and the richness conditions is satisfied. To demonstrate the effectiveness of the proposed technique it has been applied to Lorenz–Chen dynamic systems, as drive–response systems. Simulation results indicate that the proposed adaptive controller has a high performance in synchronizing two chaotic systems.
Chaos, Solitons & Fractals.
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ABSTRACT: In this paper an indirect adaptive control algorithm is proposed to stabilize the fixed points of discrete chaotic systems. It is assumed that the functionality of the chaotic dynamics is known but the system parameters are unknown. This assumption is usually applicable to many chaotic systems, such as the Henon map, logistic and many other nonlinear maps. Using the recursive-least squares technique, the system parameters are identified and based on the feedback linearization method an adaptive controller is designed for stabilizing the fixed points, or unstable periodic orbits of the chaotic maps. The stability of the proposed scheme has been shown and the effectiveness of the control algorithm has been demonstrated through computer simulations.
Chaos, Solitons & Fractals.
