Iterative Learning Control for Generalized Projective Synchronization of Fractional-order System with Unknown Local Lipschitz Function

Abstract

This paper is devoted to the generalized projective synchronization problem of fractional-order systems subject to the unknown local Lipschitz conditions. Based on the definition of the fractional integral, a suitable variable is defined, thereby the generalized projective synchronization problem between leader and follower is transformed into the stabilization problem of the system consisting of the newly defined variable. An adaptive iterative learning controller is proposed to control the fractional-order systems. Based on the composite energy function method, the convergence of learning process is analysed. Consequently, the sufficient conditions are derived to guarantee that the leader-following FOSs can achieve the generalized projective synchronization in the finite time interval as the iteration step goes to infinity. Finally, a numerical simulation example is presented to demonstrate the effectiveness of the proposed method.