Abstract:
This paper addresses the adaptive synchronization control problem for non-identical fractional-order chaotic systems with unknown parameters. Firstly, by introducing the fractional-order operator
Dp−q, the traditional integer-order projection synchronization controller is improved to achieve synchronization between the non-identical fractional order systems. Secondly, an appropriate adaptive law is developed to estimate and compensate for the unknown parameters in real time, thereby realizing robust synchronization control for fractional-order chaotic systems with parameter uncertainties. Rigorous proofs based on Lyapunov stability theory and finite-time stability theory establish the global asymptotic stability of the closed-loop system, while sufficient conditions for finite-time synchronization are derived, providing an upper bound on the settling time that explicitly depends on the system’s initial conditions. The proposed adaptive fractional projection control strategy guarantees the boundedness of synchronization errors and their convergence within a finite time. Numerical simulations demonstrate the effectiveness of the proposed synchronization scheme and its practical applicability in secure communication.