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## Adaptive synchronization of two different chaotic systems with time varying unknown parameters.(English)Zbl 1147.93397

Summary: 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 are 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.

### MSC:

 93D21 Adaptive or robust stabilization 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 93C40 Adaptive control/observation systems 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93C10 Nonlinear systems in control theory
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