Adaptive Finite-time synchronization of non-identical fractional-order chaotic systems with unknown parameters and its application in secure communication

For fractional-order chaotic systems with unknown parameters, this paper investigates the adaptive synchronization control problem of two non-identical fractional-order chaotic systems. Firstly, by introducing fractional-order operators into the synchronization controller, an improved projective synchronization scheme is proposed. Secondly, appropriate adaptive laws are designed to handle the unknown parameters in the system, making it adaptable to the design of synchronization controllers for non-identical fractional-order chaotic systems with unknown parameters. Meanwhile, based on Lyapunov stability theory and finite-time stability theory, sufficient conditions for achieving finite-time synchronization of fractional-order chaotic systems are derived, an upper bound of the settling time related to the system’s initial conditions is obtained, and the stability of the system is proven. The developed adaptive fractional projective control strategy ensures the boundedness of all synchronization errors and their stability within a finite time. Simulation results demonstrate the effectiveness of the proposed synchronization scheme and its feasibility for application in secure communication.