PDECON - Optimal Control of Ordinary, Algebraic and One-dimensional Partial
Differential Equations
Version 1.0 (1997)
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:
three different types of objective functions
numerical integration of objective functions in integral form
control approximation by piecewise constant or linear functions or
bang-bang-controls
definition of flux-functions to facilitate input
non-continous transition conditions between integration areas
(Neumann, Dirichlet, mixed)
dynamic constraints, i.e. inequality constraints depending on control and state variables
break points, where integration is restarted, e.g. to allow model changes w.r.t.
time variable
exploiting band structures
generation of 2D/3D-plot data and TEX reports
full documentation
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)