Fixed/preassigned-time stabilization and time-energy tradeoff analysis of delayed memristive reaction diffusion neural networks.

Abstract

This paper investigates the fixed-time stabilization (FS) and preassigned-time stabilization (PS) of delayed memristive reaction diffusion neural networks (MRDNNs) together with time-energy tradeoff analysis. By integrating nonsmooth analysis and Lyapunov stability theory, new stability lemmas are established to guarantee FS and PS under properly designed control schemes. Beyond theoretical stabilization, the inherent conflict between rapid convergence and control energy consumption is explicitly characterized. The controller synthesis problem is reformulated as a constrained multi-objective optimization model that jointly minimizes the theoretical settling-time bound and the cumulative control energy. An NSGA-II-based evolutionary framework is adopted to approximate the corresponding Pareto-optimal parameter sets, enabling a quantitative analysis of the time-energy tradeoff mechanism. Numerical simulations under different diffusion intensities validate the theoretical results and further reveal how spatial diffusion reshapes the structure of the time-energy tradeoff in the delayed MRDNNs.