Design of adaptive sliding mode tracking controllers for chaotic synchronization and application to secure communications

Synchronization of two identical chaotic systems with matched and mismatched perturbations by utilizing adaptive sliding mode control (ASMC) technique is presented in this paper. The sliding surface function is specially designed based on the Lyapunov stability theorem and linear matrix inequality (LMI) optimization technique. The designed tracking controller can not only suppress the mismatched perturbations when the controlled dynamics (master-slave) are in the sliding mode, but also drive the trajectories of synchronization errors into a small bounded region whose size can be adjusted through the designed parameters. Adaptive mechanisms are employed in the proposed control scheme for adapting the unknown upper bounds of the perturbations, and the stability of overall controlled synchronization systems is guaranteed. The comparison of the proposed chaotic synchronization technique with an existing generalized chaotic synchronization (GCS) method as well as application of the proposed control method to secure communications is also demonstrated in this paper.