Article | Proceedings of the 10<sup>th</sup> International Modelica Conference; March 10-12; 2014; Lund; Sweden | Efficient Implementation of Collocation Methods for Optimization using OpenModelica and ADOL-C Link�ping University Electronic Press Conference Proceedings
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Title:
Efficient Implementation of Collocation Methods for Optimization using OpenModelica and ADOL-C
Author:
Vitalij Ruge: Bielefeld University of Applied Sciences, Department of Mathematics and Engineering, Bielefeld, Germany Willi Braun: Bielefeld University of Applied Sciences, Department of Mathematics and Engineering, Bielefeld, Germany Bernhard Bachmann: Bielefeld University of Applied Sciences, Department of Mathematics and Engineering, Bielefeld, Germany Andrea Walther: Universität Paderborn, Institut für Mathematik, Paderborn, Germany Kshitij Kulshreshtha: Universität Paderborn, Institut für Mathematik, Paderborn, Germany
DOI:
10.3384/ecp140961017
Download:
Full text (pdf)
Year:
2014
Conference:
Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden
Issue:
096
Article no.:
106
Pages:
1017-1025
No. of pages:
9
Publication type:
Abstract and Fulltext
Published:
2014-03-10
ISBN:
978-91-7519-380-9
Series:
Linköping Electronic Conference Proceedings
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:
Linköping University Electronic Press; Linköpings universitet


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Efficient calculation of the solutions of nonlinear optimal control problems (NOCPs) is becoming more and more important for today’s control engineers. The systems to be controlled are typically described using differential-algebraic equations (DAEs); which can be conveniently formulated in Modelica. In addition; the corresponding optimization problem can be expressed using Optimica.

Solution algorithms based on collocation methods are highly suitable for discretizing the underlying dynamic model formulation. Thereafter; the corresponding discretized optimization problem can be solved; e.g. by the interior-point optimizer Ipopt. The performance of the optimizer heavily depends on the availability of derivative information for the underlying optimization problem. Typically; the gradient of the objective function; the Jacobian of the DAEs as well as the Hessian matrix of the corresponding Lagrangian formulation need to be determined. If only some or none of these derivatives are provided; usually numerical approximations are used by the optimizer internally.

OpenModelica supports the Optimica language and is capable of automatically generating the discretized optimization problem using collocation methods as well as the whole symbolic machinery available. In addition; all necessary derivative information is determined using the automatic differentiation capabilities of ADOL-C; which has now been integrated into the OpenModelica environment.

Keywords: Modelica; optimization; automatic differentiation; collocation; OpenModelica; ADOL-C

Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden

Author:
Vitalij Ruge, Willi Braun, Bernhard Bachmann, Andrea Walther, Kshitij Kulshreshtha
Title:
Efficient Implementation of Collocation Methods for Optimization using OpenModelica and ADOL-C
DOI:
http://dx.doi.org/10.3384/ecp140961017
References:

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Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden

Author:
Vitalij Ruge, Willi Braun, Bernhard Bachmann, Andrea Walther, Kshitij Kulshreshtha
Title:
Efficient Implementation of Collocation Methods for Optimization using OpenModelica and ADOL-C
DOI:
http://dx.doi.org/10.3384/ecp140961017
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