## PDECON: A FORTRAN Code for Solving Optimal
Control Problems Based on Ordinary, Algebraic and
Partial Differential Equations

M. Blatt, K. Schittkowski: Report, Dept. of Mathematics, University of Bayreuth (1997)

**Abstract:**
We describe a FORTRAN code with name PDECON that can be used to solve
optimal control problems governed by systems of one-dimensional
time-dependent partial differential equations
and coupled ordinary differential equations.
Three different types of cost functions are available,
and it is possible to define constraints for state, control and additional
discrete, i.e. time-independent variables.
Control functions are approximated by piecewise constant or piecewise
linear functions. Alternatively bang-bang controls can be handled.
Since the final integration time is allowed to become an optimization parameter,
PDECON solves also time-optimal control problems.
The line method is used to discretize partial differential
equations transforming the original
system into a system of ordinary differential equations.
Discretized differential equations and coupled ordinary differential
or differential algebraic equations are solved by standard explicit or
implicit integration methods.

Thus, the optimal control problem is transformed into
a nonlinear programming problem which is solved by a sequential
quadratic programming method.
Time-dependent inequality constraints are discretized w.r.t. given break
points.

We outline the mathematical formulation of the optimal control problem
that can be solved numerically by PDECON, describe the program organisation
and usage, and present a couple of examples, most of them with some
practical background.
Especially we show how to solve a control problem where the
diffusion of a substance through the skin is controlled by an external
electrical field.