Numerical Optimal Control of Parabolic PDES Using DASOPT

This paper gives a preliminary description of DASOPT, a software system for the optimal control of processes described by time-dependent partial differential equations (PDEs). DASOPT combines the use of efficient numerical methods for solving differential-algebraic equations (DAEs) with a package for large-scale optimization based on sequential quadratic programming (SQP). DASOPT is intended for the computation of the optimal control of time-dependent nonlinear systems of PDEs in two (and eventually three) spatial dimensions, including possible inequality constraints on the state variables. By the use of either finite-difference or finite-element approximations to the spatial derivatives, the PDEs are converted into a large system of ODEs or DAEs. Special techniques are needed in order to solve this very large optimal control problem. The use of DASOPT is illustrated by its application to a nonlinear parabolic PDE boundary control problem in two spatial dimensions. Computational results with and without bounds on the state variables are presented.