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Parallel Multiple-Shooting and Collocation Optimization with OpenModelica

Nonlinear model predictive control (NMPC) has be-come increasingly important for today’s control engi-neers during the last decade. In order to apply NMPC a nonlinear optimal control problem (NOCP) must be solved which in general needs high computational ef-fort. State-of-the-art solution algorithms are based on multiple shooting or collocation algorithms, which are required to solve the underlying dynamic model formu-lation. 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 colloca-tion 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 descrip-tion has been done in Optimica and Modelica. The simulation has been performed using OpenModelica. Speedup curves for parallel execution are presented.

Bernhard Bachmann, Lennart Ochel, Vitalij Ruge, Mahder Gebremedhin, Peter Fritzson, Vaheed Nezhadali, Lars Eriksson and Martin Sivertsson


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