Novel predefined-time control for fractional-order systems and its application to chaotic synchronization

Based on the fractional calculus and sliding mode control (SMC) techniques, this paper presents a predefined-time synchronization scheme for fractional-order chaotic systems (FOCSs). Firstly, a predefined-time control method is proposed for fractional-order systems. Subsequently, a novel sliding surface is presented to ensure predefined-time convergence of the synchronization error. Then, a controller is designed by combining the predefined-time stability and the SMC method to ensure that the synchronization error converges to zero within the predefined time. Finally, the feasibility and robustness of the scheme are illustrated with two numerical simulation examples.