Fuzzy sliding mode control based-fast finite-time projective synchronization for fractional-order chaotic systems

This study explores the challenge of achieving a fast finite-time projective synchronization (FFTPS) in chaotic systems characterized by incommensurate fractional orders, unknown master-slave models, and uncertain external disturbances. Utilizing the principles of Lyapunov stability theory, two fuzzy sliding mode control (FSMC) schemes are proposed. Accordingly, two novel non-singular finite-time sliding surfaces are constructed. Fuzzy logic systems are utilized to provide an approximation of the continuous uncertain dynamics within the master-slave system. The sufficient conditions for both controllers are derived to ensure this robust FFTPS. Finally, the proposed controllers are validated through numerical simulations on two projective synchronization examples of fractional-order chaotic systems, demonstrating their feasibility.