Conference article

Parallel Multiple-Shooting and Collocation Optimization with OpenModelica

Bernhard Bachmann
Dept. Mathematics and Engineering, University of Applied Sciences, Bielefeld, Germany

Lennart Ochel
Dept. Mathematics and Engineering, University of Applied Sciences, Bielefeld, Germany

Vitalij Ruge
Dept. Mathematics and Engineering, University of Applied Sciences, Bielefeld, Germany

Mahder Gebremedhin
PELAB – Programming Environment Lab, Dept. Computer Science Linköping University, Linköping, Sweden

Peter Fritzson
PELAB – Programming Environment Lab, Dept. Computer Science Linköping University, Linköping, Sweden

Vaheed Nezhadali
Vehicular Systems, Dept. Electrical Engineering Linköping University, Linköping, Sweden

Lars Eriksson
Vehicular Systems, Dept. Electrical Engineering Linköping University, Linköping, Sweden

Martin Siversson
Vehicular Systems, Dept. Electrical Engineering Linköping University, Linköping, Sweden

Download articlehttp://dx.doi.org/10.3384/ecp12076659

Published in: Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany

Linköping Electronic Conference Proceedings 76:67, s. 659-668

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Published: 2012-11-19

ISBN: 978-91-7519-826-2

ISSN: 1650-3686 (print), 1650-3740 (online)

Abstract

Nonlinear model predictive control (NMPC) has become increasingly important for today’s control engineers during the last decade. In order to apply NMPC a nonlinear optimal control problem (NOCP) must be solved which needs a high computational effort.

State-of-the-art solution algorithms are based on multiple shooting or collocation algorithms; which are required to solve the underlying dynamic model formulation. This paper describes a general discretization scheme applied to the dynamic model description which can be further concretized to reproduce the mul-tiple shooting or collocation approach. Furthermore; this approach can be refined to represent a total collocation method in order to solve the underlying NOCP much more efficiently. Further speedup of optimization has been achieved by parallelizing the calculation of model specific parts (e.g. constraints; Jacobians; etc.) and is presented in the coming sections.

The corresponding discretized optimization problem has been solved by the interior optimizer Ipopt. The proposed parallelized algorithms have been tested on different applications. As industrial relevant application an optimal control of a Diesel-Electric power train has been investigated. The modeling and problem description has been done in Optimica and Modelica. The simulation has been performed using OpenModelica. Speedup curves for parallel execution are presented.

Keywords

Modelica; Optimica; optimization; multiple shooting; collocation; parallel; simulation

References

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