Stabilization of delayed stochastic reaction-diffusion Cohen-Grossberg neural networks via variable gain intermittent boundary control.

Abstract

This study presents a novel variable gain intermittent boundary control (VGIBC) approach for stabilizing delayed stochastic reaction-diffusion Cohen-Grossberg neural networks (SRDCGNN). In contrast to traditional constant gain intermittent boundary control (CGIBC) methods, the proposed VGIBC framework dynamically adjusts the control gain based on the operational duration within each control cycle, thereby improving adaptability to variations in work interval lengths. The time-varying control gain is designed using a piecewise interpolation method across work intervals, defined by a finite set of static gain matrices. To address the switching dynamics of the intermittently controlled neural networks and exploit the flexibility offered by the dynamic control gain, a piecewise Lyapunov function is employed to fit the dynamic structure of the control gain. By applying distinct Razumikhin-based solution estimation techniques: one tailored to active control periods and the other to rest periods, new mean square intermittent stabilization criteria are derived that show reduced conservatism compared to CGIBC-based results. The optimal control gain function is determined by solving a convex optimization procedure that minimizes the control rate at a given level of gain norm limitation. The efficacy of the proposed VGIBC strategy is validated through two numerical examples.