Fixed-Time Anti-Synchronization of Unified Chaotic Systems via Adaptive Backstepping Approach

In this brief, the fixed-time anti-synchronization control problem is considered for two unified chaotic systems with uncertain parameters. In the process of controller design, adaptive technique is applied to approximate the uncertain constants occurred in the original systems and the piecewise functional approach is introduced to overcome the singularity problem appeared in the virtual control signals. Based on the Lyapunov theory and fixed-time control method, an adaptive fixed-time control scheme is designed. The designed controller achieves the anti-synchronization of two unified chaotic systems in a fixed-time. Theoretical analysis and simulation results demonstrate that the effectiveness of the control method.