New Predefined Time Sliding Mode Control Scheme for Multi-Switch Combination–Combination Synchronization of Fractional-Order Hyperchaotic Systems

A new predefined time sliding mode control theme is proposed and applies to the multi-switch combination–combination synchronization (MSCCS) of fractional-order (FO) hyperchaotic systems. Firstly, based on the Lyapunov stability theory, we demonstrate the effectiveness of our proposed predefined time sliding mode control theme. Meanwhile, based on the new predefined time control strategy, we propose new sliding mode surfaces and controllers to achieve the MSCCS of FO hyperchaotic systems. Considering the system’s external environment’s complexity in practical applications, the parameter uncertainties and external disturbances are added to the FO hyperchaotic system. Through the final numerical simulation, the predefined time slide mode controller proposed in this paper can make the drive–response systems reach the predefined time synchronization, thus proving the effectiveness of the control strategy and its robustness to some unfavorable factors, such as external perturbations.