A direct multiple shooting method for the numerical solution of optimal control and parameter estimation problems


PAREST is a direct multiple shooting method designed to solve parameter estimation and optimal control problems in systems of differential-algebraic equations or ordinary differential equations.

In parameter estimation problems parameters of the dynamic model are fitted to a set of measurements of (functions of) the state variables by minimizing a nonlinear least squares objective.
In optimal control problems the optimal control variable is computed that minimizes a performance index of Mayer type.
In both cases, inequality constraints may be imposed on the state and control variables as well.

PAREST is a direct transcription method. I. e. a multiple shooting approach is used to discretize and solve the boundary value problem. The control variables are discretized by piecewise linear functions.
The generalized Gauss-Newton method NLSCON (check CodeLib of eLib for information) and the Sequential Quadratic Programming methods NPSOL and NLSSOL are used to solve the resulting nonlinearly constrained least squares and nonlinearly constrained optimization problems.
Please note that NLSCON, NPSOL and NLSSOL are not distributed by us.

The software consists of a numerical core written in Fortran 77 and a main program written in C for handling input and output. The user must provide subroutines that define the model functions (objective, differential equations, boundary conditions, nonlinear inequality constraints). This is usually done by editing the pre-defined subroutines in the file uspec.f (Fortran 77). Further informations on the problem (as the dimensions of the problem, specifications of the numerical methods, lower and upper bounds for all variables, optional scaling, the three time grids (of the multiple shooting discretization, of the control discretization, and of the times of measurements (only in parameter identification)) as well as initial estimates of state and control variables, the measurement values (only in parameter estimation)) have to be supplied by editing the input file start.dat.

A supplementary program PGRAPH is provided which supports a visualization of the numerical results using the LRZ-graphics library.

Note: Up to now, PAREST has only been installed on Unix systems (e.g., SunOS, IRIX, Linux).

Publications related to the method:

Examples of applications of the method:

Licensing policy

The software PAREST is not in the public domain. However, it is available for license, without fee, for education and non-profit research purposes. Please contact the author at the address given below.

Any entity desiring permission to incorporate this software or a work based on the software into commercial products or otherwise use it for commercial purposes should also contact:

Prof. Dr. Oskar von Stryk
Fachgebiet Simulation und Systemoptimierung (Simulation and Systems Optimization Group)
Fachbereich Informatik (Department of Computer Science)
Technische Universität Darmstadt
D-64283 Darmstadt, Germany
E-Mail (preferred): stryk(at)
Phone: +49 6151-16-2513
Fax: +49 6151-16-6648

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