Optimal control of partial differential equations based on the Variational Iteration Method

Abstract

In this work, the Variational Iteration Method is used to solve a quadratic optimal control problem of a system governed by linear partial differential equations. The idea consists in deriving the necessary optimality conditions by applying the minimum principle of Pontryagin, which leads to the well-known Hamilton–Pontryagin equations. These linear partial differential equations constitute a multi-point-boundary value problem. To achieve the solution of the Hamilton–Pontryagin equations using the Variational Iteration Method, an approach is proposed and illustrated by two application examples.