DAE Approximations of PDE Modeled Control Problems

Over the last decade there has been substantial progress on the development of theory and numerical methods for implicit systems of differential and algebraic equations (DAEs). In many control applications involving PDE models it is standard engineering practice to replace the PDEs by a finite dimensional system of ordinary differential equations. There are a variety of ways to do this approximation. Sometimes this approximation forms a DAE. While there has been a substantial amount of work on infinite dimensional control problems, there has been less attention paid to how the choice of approximation relates to the numerical and analytic properties of the finite dimensional DAE control system. In this paper we discuss some of the issues involved in this relationship.