Predefined-time stability scheme based on sliding mode control

In this study, the problem of synchronizing same-dimensional heterogeneous chaotic systems under disturbances is solved by introducing a synchronization control method based on predefined-time stability theory. First, a new sufficient condition for achieving stability within a predefined time range is established on the basis of the Lyapunov theory, and an integral sliding surface is constructed, which successfully eliminates the arrival phase that is commonly observed in the traditional predefined-time sliding surfaces. Next, robust control strategies with disturbance compensation are designed for two different cases: a system affected by disturbances and a system that is not affected. These controllers are particularly capable of explicitly specifying an upper bound for the time required for convergence. Finally, numerical simulation experiments are performed to verify the effectiveness of the proposed control approach. Comparative experiments show that this approach surpasses the state-of-the-art methods, especially in terms of convergence speed and robustness.