Fuzzy logic embedding of fractional order sliding mode and state feedback controllers for synchronization of uncertain fractional chaotic systems

Abstract

This paper studies the synchronization of a class of uncertain fractional order (FO) chaotic systems that is applicable in secure communication. A novel hybrid FO controller, based on sliding mode and state feedback techniques combined with fuzzy logic, is developed. The algorithm, derived via the fractional Lyapunov theory, guarantees the stability of the overall system and the convergence of the synchronization errors toward a small residual set. Simulations demonstrate the capability of the proposed control algorithm in secure communications, not only in terms of speed of response, but also by reducing the chattering phenomenon.