Theoretical and Computational Issues of Optimal Control for Distributed Hopfield Neural Network Equations with Diffusion Term
Quan‐Fang Wang · SIAM Journal on Scientific Computing · 2007
This work investigates theoretical and computational issues of optimal control for distributed Hopfield neural network equations with diffusion term. Due to introducing a diffusion term in our model, a theoretical conclusion is deduced for the control of the nonlinear parabolic partial differential equation in the framework of variational methods (cf. [J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer‐Verlag, Berlin, Heidelberg, New York, 1971]) by means of distributed control, boundary control, and initial control. Experimental demonstration is implemented via a semidiscrete numerical algorithm based on the finite element method. The theoretical results are verified using the proposed scheme.