PDECON - Optimal Control of Ordinary, Algebraic and One-dimensional Partial Differential Equations

 

Purpose:

PDECON solves optimal control problems based on a system of ordinary differential equations, differential algebraic equations or one-dimensional, time-dependent and algebraic partial differential equations.

Numerical Method:

The line method is applied to discretize the system w.r.t. the spatial variable, to get a system of ordinary differential equations. To approximate spatial derivatives, polynomial approximation, difference formulae and special upwind formulae (TVD or similar) for hyperbolic equations are implemented. Systems of ordinary differential equations are solved by standard methods for stiff- and non-stiff equations, e.g. by some routines of Hairer and Wanner. State and control constraints in inequality form are discretized w.r.t. time variable. The resulting constrained nonlinear programming problem is solved by the SQP algorithm NLPQL. Gradients of objective function and constraint are approximated by forward differences or internal numerical differentiation.

Program Organization:

PDECON is a double precision FORTRAN-77 subroutine and all parameters are passed through arguments. An additional main program takes over some organizational ballast and reads in all problem data. A user provided subroutine is required to define initial values, constraints, partial differential equations together with suitable boundary conditions or coupled ordinary equations and objective function.

Special Features:

1. three different types of objective functions
2. numerical integration of objective functions in integral form
3. control approximation by piecewise constant or linear functions or bang-bang-controls
4. definition of flux-functions to facilitate input
5. non-continous transition conditions between integration areas (Neumann, Dirichlet, mixed)
6. dynamic constraints, i.e. inequality constraints depending on control and state variables
7. break points, where integration is restarted, e.g. to allow model changes w.r.t. time variable
8. exploiting band structures
9. generation of 2D/3D-plot data and TEX reports
10. full documentation
11. FORTRAN source code
    

Applications:

PDECON is in practical use to control transdermal processes in pharmaceutical models (Boehringer Ingelheim), and to control chemical turbular reactors (BASF).

Reference:

M. Blatt, K. Schittkowski, PDECON: A FORTRAN code for solving optimal control problems based on ordinary, algebraic and partial differential equations, Report, Dep. of Mathematics, University of Bayreuth (1997)

Availability:

For more details contact the author.