Finite-time bipartite synchronization for coupled neural networks: An aperiodically intermittent and impulsive control approach

Abstract

This paper delves into the issue of finite-time bipartite synchronization of neural networks (NNs) with signed graphs. A novel hybrid control approach, incorporating aperiodically intermittent control (AIC) and impulsive control (IC), is presented. This strategy significantly reduces the control costs and the duration of continuous input control in the networks. Firstly, the sufficient conditions and settling time for the system to reach finite-time synchronization under AIC are presented using a Lyapunov function. Moreover, the integration of IC into the coupled NNs is explored. On the one hand, the synchronization speed of coupled NNs is accelerated by assuming that the IC occurs within the controlled segments of the AIC. On the other hand, when the IC occurs in the uncontrolled segments of the AIC, it can diminish the controlled periods of the AIC. Subsequently, based on the two hybrid controllers designed above, the synchronization criteria for the coupled NNs are established and the corresponding settling time is estimated. Finally, examples are provided to corroborate the efficacy of the designed AIC and IC.

Keywords Aperiodically intermittent control, Coupled neural networks, Finite-time bipartite synchronization, Impulsive control