Finite Elements and Terminal Penalization for Quadratic Cost Optimal Control Problems Governed by Ordinary Differential Equations

Abstract

We use the finite element method to compute optimal controls of systems governed by linear ordinary differential equations with a quadratic performance index. As an application we use the penalty technique to solve terminal state optimal controllability problems. Numerical instabilities, which are common in the use of penalty, are minimized when the finite element method is applied to solve this problem. Convergence theorems are given and error and penalty parameter estimates are presented. Concrete examples for various situations are given to illustrate the theory.