Constrained Synchronization of Drive and Response Chaotic Systems with Parametric Uncertainty using Barrier Lyapunov Function

This paper presents a systematic control design methodology for the synchronization of a class of chaotic systems configured as the drive and response systems. We achieve state synchronization with a predefined bound on the state errors by exploiting the idea of barrier Lyapunov function and considering parametric uncertainties in the response system. Under a mild assumption on the initial state errors, we prove the asymptotic convergence of state errors to the origin. We also obtain explicit bounds on the state errors and estimated uncertain parameters in the post-design analysis. Simulations are carried out for Lü chaotic system to illustrate the adequacy of the proposed controller and the uncertain parametric estimator.