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.
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