Computation issue of pointwise controls for diffusion Hopfield neural network system

This paper consider the pointwise controls problem of Hopfield neural network equation with diffusion term subject to quadratic criteria in the framework of variational method. Based on established optimal control theory to pointwise case, numerical study is carried out by constructing a semi-discrete algorithm with continuous time. Furthermore, for given point control inputs, the optimal pointwise controls are obtained to achieve the minimization. Experiments demonstration is implemented for verifying proposed algorithm.