Adaptive finite-time synchronization of fractional-order memristor chaotic system based on sliding-mode control

In this paper, based on sliding-mode control, a finite-time adaptive synchronization method is introduced to realize the generalized projective synchronization of fractional-order memristor chaotic systems with unknown parameters. First, a class of memristor chaotic system is extended to fractional order, and the chaos characteristics of the system are studied. Then a new fractional-order integral sliding-mode surface with faster convergence speed is designed, which can make the error system converge to zero in finite time. Next the controller with adjustable parameters and the adaptive laws are designed, and the sufficient condition for the sliding-mode surface can be reached by the synchronization error system in finite time and the unknown parameters can be identified in finite time is obtained. Finally, the numerical simulations show that the generalized projection synchronization and unknown parameter identification of fractional-order memristor chaotic system can be realized in a short time under the proposed synchronization strategy.