Adaptive fixed-time output synchronization of MWRDNNs with delayed output couplings

Abstract

This work develops an adaptive output feedback control technique to make multi-weight reaction–diffusion neural networks (MWRDNNs) with delayed output couplings be fixed-time output synchronized. Unlike earlier related works, the proposed control algorithm introduces an adaptive law to timely update the control gain of the node, avoiding dependence on global information of the network. Additionally, the algorithm incorporates integral terms with multiple coupling delays, mitigating the impact of multiple coupling delays in the network. By adopting the Lyapunov functional method, fixed-time stability theory, and key inequality techniques, the fixed-time output synchronization (OS) criterion is derived, and the settling time is obtained, which avoids the defect of relying on the initial value of the system. Concurrently, a corollary states that the fixed-time OS can be reached for MWRDNNs without output coupling delays through a node-based adaptive adjustment scheme. Lastly, the effectiveness of the developed control methods is validated by the correlation results obtained from two numerical simulation examples.