Synchronization for fractional-order neural networks with full/under-actuation using fractional-order sliding mode control

This paper considers synchronization between two fractional-order neural networks (FONNs). To handle the case of full/under-actuation, i.e. the dimension of the synchronization controller is equal to or less than that of the FONNs, a novel fractional-order integral sliding surface is designed, and the feasibility of the proposed approach is shown by solving two linear matrix inequalities. Then, based on the fractional Lyapunov stability criterion, a fractional-order sliding mode controller equipped with fractional-order adaptation laws is constructed to guarantee the synchronization error converging to an arbitrary small region of the origin. The effectiveness of the proposed control method is verified by two simulation examples.