An Artificial Neural Network for Solving Distributed Optimal Control of the Poisson’s Equation

摘要

This paper presents a simple and efficient method based on artificial neural network to solve distributed optimal control of Poisson’s equation with Dirichlet boundary condition. The trial solutions are used to approximate the state and control variables. These trial solutions are considered by using a single layer neural network. By replacing the trial solutions in objective function and Poisson’s equation, then using the weighted residual method, distributed optimal control of Poisson’s equation is converted to a linear quadratic optimal control problem. The weights of the trial solutions are computed by solving the new problem. In order to solve the linear quadratic optimal control problem, the Pontryagin maximum principle is used. Finally we apply the proposed method on several examples that in computational experiments, the high efficiency of the presented method is illustrated.