Global projective synchronization in finite time of nonidentical fractional-order neural networks based on sliding mode control strategy

In this paper, a novel fractional-order sliding mode control strategy is introduced to synchronize two nonidentical fractional order neural networks (FNNs) in finite time. Firstly, by applying fractional-order calculation, the properties of the global asymptotical stability and convergence in finite time are developed for the fractional-order differential equation system. Secondly, based on the proposed principle of convergence in finite time, a new fractional-order sliding mode surface is presented and its global stability in finite time is analytically proved. In addition, an appropriate sliding mode controller is designed to drive the state trajectories of error system to the prescribed sliding surface in finite time and remain on it evermore. Meanwhile, by means of the fractional Lyapunov-like approach, the global projective synchronization condition is given, and the synchronization time is explicitly evaluated. As the special case, some sufficient conditions are given to guarantee global complete synchronization, anti-synchronization and stabilization of nonidentical FNNs. Finally, an example is given to demonstrate the validity of the proposed method.