An adaptive approach to the control and synchronization of continuos-time chaotic systems

This paper is concerned with synchronization and control of chaotic nonlinear dynamical systems. First, a unified frame for both the synchronization and the control problem is described. Then by modifying a feedback plus feedforward controller, a discontinuous strategy is synthesized which exploits the boundedness of chaotic attractors and limit cycles. Finally, an adaptive approach is investigated and an adaptive estimation law is implemented. The result, which is both global and not reliant on complete knowledge of the systems involved, is rigorously proved by means of Lyapunov Theory. An application to the synchronization of two chaotic systems is presented.