Abstract
This paper is concerned with the finite-time chaotic synchronization and dynamic errors in finite-time stabilization of master-slave systems. We suggest solving these issues using a virtual recursive adaptive nonlinear controller when different unknown parameters occur. Therefore, a systematic design approach is defined for constructing both virtual adaptive nonlinear feedback control laws and associated Lyapunov functions. The corresponding sufficient conditions to achieve synchronization between two chaotic systems are obtained based on the Lyapunov stability theory. Then, two applications are evaluated using our approach: Genesio-Tesi and Coullet systems which are two topologically dissimilar systems, known as difficult to synchronize. The results presented in this paper demonstrate both effectiveness and feasibility of our control laws.
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