Mixed $$H_\infty $$ H ∞ /Passive Projective Synchronization for Nonidentical Uncertain Fractional-Order Neural Networks Based on Adaptive Sliding Mode Control

Abstract

This paper deals with the problem of mixed $$H_\infty $$ /passive projective synchronization for two different fractional-order (FO) neural networks with uncertain parameters. Firstly, a fractional integral sliding surface which is suitable for the considered FO error system is proposed. Secondly, in terms of the established sliding surface, combining a novel reaching law, a new adaptive sliding mode control law is introduced, which can force the closed-loop dynamic error system trajectories to reach the sliding surface. Then, a continuous frequency distributed model of the FO dynamic networks is given, via the application of FO system stability theory and robust control, the projective synchronization conditions are addressed in terms of linear matrix inequality techniques. Based on the conditions, a desired controller which can guarantee the robust stability of the closed-loop system and also ensure a mixed $$H_\infty $$ /passive performance level is designed. Finally, synchronization of two nonidentical FO neural networks with uncertain parameters as a simulation example is given to illustrate the effectiveness and advantages of the proposed method.