Fixed-Time Adaptive Synchronization of Uncertain Chaotic Systems

This article investigates the practically fixed-time synchronization problem for uncertain chaotic systems. First, a practically fixed-time stability criterion is introduced. Based on this criterion, an adaptive backstepping control technique is employed to design the controller. Unlike traditional dynamic surface control strategies, the proposed approach incorporates a continuous piecewise function. Theoretical analysis demonstrates that the proposed control strategy ensures the practically fixed-time stability of the closed-loop system, with the synchronization error converging to a small neighborhood of the origin within a fixed time. Finally, a simulation example is provided to verify the feasibility and effectiveness of the proposed method.