Konferensartikel

Symbolic Transformations of Dynamic Optimization Problems

Fredrik Magnusson
Department of Automatic Control, Lund University, Lund, Sweden

Karl Berntorp
Department of Automatic Control, Lund University, Lund, Sweden

Björn Olofsson
Department of Automatic Control, Lund University, Lund, Sweden

Johan Åkesson
Department of Automatic Control, Lund University, Lund, Sweden/Modelon AB, Ideon Science Park, Lund, Sweden

Ladda ner artikelhttp://dx.doi.org/10.3384/ecp140961027

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

Linköping Electronic Conference Proceedings 96:107, s. 1027-1036

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Publicerad: 2014-03-10

ISBN: 978-91-7519-380-9

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

Abstract

Dynamic optimization problems involving differential-algebraic equation (DAE) systems are traditionally solved while retaining the semi-explicit or implicit form of the DAE. We instead consider symbolically transforming the DAE into an ordinary differential equation (ODE) before solving the optimization problem using a collocation method. We present a method for achieving this; which handles DAE-constrained optimization problems. The method is based on techniques commonly used in Modelica tools for simulation of DAE systems.

The method is evaluated on two industrially relevant benchmark problems. The first is about vehicletrajectory generation and the second involves startup of power plants. The problems are solved using both the DAE formulation and the ODE formulation and the performance of the two approaches is compared. The ODE formulation is shown to have roughly three times shorter execution time. We also discuss benefits and drawbacks of the two approaches.

Nyckelord

Dynamic optimization; symbolic transformations; causalization; collocation

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