The paper presents an adaptive pre-defined sliding mode control (SMC) law for the synchronization of two multi-wing chaotic systems. To ensure the settling of the error system’s state within a pre-defined time, a sufficient condition is introduced based on Lyapunov theory. The proposed control law incorporates a pre-defined nonlinear sliding surface with an adaptive reaching law, where the parameters of the sliding surface depend on the pre-defined time to guarantee convergence within that time frame. The adaptation of the discontinuous gain in the proposed reaching law is achieved through a positive semi-definite barrier function. The stability analysis of the proposed control law confirms the pre-defined convergence time. A performance comparison between the proposed control law and an established control law, carried out through numerical simulations, demonstrates its superiority and suitability for nonlinear tracking problems. Furthermore, the proposed pre-defined SMC law is applied to image encryption and decryption to demonstrate its applicability in practical operations.
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