Article | Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany | Parallel Multiple-Shooting and Collocation Optimization with OpenModelica

Title:
Parallel Multiple-Shooting and Collocation Optimization with OpenModelica
Author:
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 ‚Äď Programming Environment Lab, Dept. Computer Science Link√∂ping University, Link√∂ping, Sweden Peter Fritzson: PELAB ‚Äď Programming Environment Lab, Dept. Computer Science Link√∂ping University, Link√∂ping, Sweden Vaheed Nezhadali: Vehicular Systems, Dept. Electrical Engineering Link√∂ping University, Link√∂ping, Sweden Lars Eriksson: Vehicular Systems, Dept. Electrical Engineering Link√∂ping University, Link√∂ping, Sweden Martin Siversson: Vehicular Systems, Dept. Electrical Engineering Link√∂ping University, Link√∂ping, Sweden
DOI:
10.3384/ecp12076659
Download:
Full text (pdf)
Year:
2012
Conference:
Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany
Issue:
076
Article no.:
067
Pages:
659-668
No. of pages:
10
Publication type:
Abstract and Fulltext
Published:
2012-11-19
ISBN:
978-91-7519-826-2
Series:
Linköping Electronic Conference Proceedings
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:
Linköping University Electronic Press; Linköpings universitet


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

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

Author:
Bernhard Bachmann, Lennart Ochel, Vitalij Ruge, Mahder Gebremedhin, Peter Fritzson, Vaheed Nezhadali, Lars Eriksson, Martin Siversson
Title:
Parallel Multiple-Shooting and Collocation Optimization with OpenModelica
DOI:
10.3384/ecp12076659
References:
[1] Open Source Modelica Consortium. OpenModelica System Documentation Version 1.8.1; April 2012. http://www.openmodelica.org
[2] Modelica Association. The Modelica Language Specification Version 3.2; March 24th 2010. http://www.modelica.org. Modelica Association. Modelica Standard Library 3.1. Aug. 2009. http://www.modelica.org.
[3] Jasem Tamimi; Pu Li. A combined approach to nonlinear model predictive control of fast systems. Journal of Process Control; 20; pp 1092‚Äď1102; 2010. doi: 10.1016/j.jprocont.2010.06.002.
[4] Biegler; Lorenz T. 2010. Nonlinear Programming: Concepts; Algorithms; and Applications to Chemical Processes. s.l.: Society for Industrial Mathematics; 2010. doi: http://dx.doi.org/10.1137/1.9780898719383.
[5] Munz; Claus-Dieter and Westermann; Thomas. 2009. Numerische Behandlung gewöhlicher und partieller Differenzialgleichungen. Berlin Heideberg : Springer Verlag; 2009
[6] Heuser; Harro. 2006. Gewöhnliche Differential-gleichungen. Wiesbaden : Teubner Verlag; 2006.
[7] Tamimi; Jasem. 2011. Development of Efficient Algorithms for Model Predictive Control of Fast Systems. D√ľsseldorf: VDI Verlag; 2011.
[8] Friesz; Terry L. 2007. Dynamic Optimization and Differential Games. US: Springer US; 2007.
[9] Folkmar; Bornemann und Deuflhard; Peter. 2008. Numerische Mathematik: Numerische Mathematik 2: Gewöhnliche Differentialgleichungen: Bd II: [Band] 2. s.l. : Gruyter; 2008.
[10] Martin Sivertsson and Lars Eriksson Optimal power response of a diesel-electric powertrain. Submitted to ECOSM’12; Paris; France; 2012.
[11] Braun; Willi; Ochel Lennart and Bachmann Bernhard. Symbolically Derived Jacobians Using Automatic Differentiation - Enhancement of the OpenModelica Compiler; Modelica Conference 2011. doi: 10.3384/ecp11063495.
[12] Joel Andersson; Johan √Ökesson; Moritz Diehl; CasADi - A symbolic package for automatic differentiation and optimal control; Proc. 6th International Conference on Automatic Differentia-tion; 2012.
[13] Houska; B.; Ferreau; H.J.; and Diehl; M. (2011). ACADO toolkit - an open source framework for automatic control and dynamic optimization. Op-timal Control Applications & Methods; 32(3); 298-312. doi: 10.1002/oca.939.
[14] Functional Mock-up Interface: http://www.functional-mockup-interface.org/index.html
[15] Johan √Ökesson. Optimica‚ÄĒAn Extension of Modelica Supporting Dynamic Optimization. In 6th International Modelica Conference 2008. Modelica. Association; March 2008
[16] Interior Point OPTimizer (Ipopt) https://projects.coin-or.org/Ipopt

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

Author:
Bernhard Bachmann, Lennart Ochel, Vitalij Ruge, Mahder Gebremedhin, Peter Fritzson, Vaheed Nezhadali, Lars Eriksson, Martin Siversson
Title:
Parallel Multiple-Shooting and Collocation Optimization with OpenModelica
DOI:
10.3384/ecp12076659
Note: the following are taken directly from CrossRef
Citations:
  • Alachew Shitahun, Vitalij Ruge, Mahder Gebremedhin, Bernhard Bachmann, Lars Eriksson, Joel Andersson, Moritz Dieh & Peter Fritzson (2013). Model-Based Dynamic Optimization with OpenModelica and CasADi. IFAC Proceedings Volumes, 46(21): 446. DOI: 10.3182/20130904-4-JP-2042.00166