Adaptive Boundary Control for Synchronization of Reaction–Diffusion Neural Networks With Random Time-Varying Delay

This article addresses the synchronization problem of reaction-diffusion neural networks (RDNNs) with random time-varying delay (RTVD) via boundary control (BC) (including adaptive BC and BC with constant-valued gain) under distributed measurements or boundary measurements. First, a novel BC strategy with constant-valued gain is designed, which considers three cases of the measurements, that is, distributed measurements, boundary measurements, and both coexist. Subsequently, an adaptive BC scheme under boundary measurements is proposed, where the control gain is regulated effectively. Next, based on the inequality techniques and Lyapunov direct approach, the delay-dependent synchronization conditions are gained and some linear matrix inequalities (LMIs) based theorems are given. Then, the BC design for the delayed RDNNs is transformed into an LMI feasibility problem. Finally, the developed BC approaches are validated by the simulation results.