A Collocation Method for Quadratic Control Problems Governed by Ordinary Elliptic Differential Equations

Abstract

We investigate discretizations for a class of quadratic optimal control problems governed by one-dimensional elliptic differential equations. In contrast to the papers [3] dealing with finite element approximations and [2, 1] dealing with finite difference approximation, the dicretizations considered here are based on a collocation method using quadratic splines for the state equation. Under the assumption that the optimal control has bounded variation we prove discrete and continuous quadratic convergence of approximating controls.