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.


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