Abstract

This paper proposes an adaptive robust finite-time control method based on ‎global sliding surface for the synchronization of a class of chaotic systems. New chattering-‎free control laws are designed to guarantee the removal of the reaching mode and realize ‎the existence of the sliding mode around the designed surface right from the first moment. ‎The proposed adaptive-tuning controllers eliminate the requirement of the knowledge about ‎disturbance bounds. Using the suggested control technique, the superior master-slave ‎synchronization is achieved, the chattering problem is fully solved, and the amplitudes of ‎the control signals are noticeably decreased. Demonstrative simulation results on Lü chaotic ‎system are presented to indicate the efficiency and usefulness of the proposed scheme. In ‎the end, using a state-feedback controller, we obtain a four dimensional system with two ‎interesting features. First, some hyperchaotic solutions are proposed and then, a continuous ‎bifurcation diagram showing chaos for a wide range of bifurcation parameter is presented.‎