Symbolic Transformations of Dynamic Optimization Problems

Fredrik Magnusson, Karl Berntorp, Björn Olofsson, Johan Åkesson

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingpeer-review

167 Downloads (Pure)


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 vehicle-trajectory 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.
Original languageEnglish
Title of host publicationProceedings of the 10th International Modelica Conference
PublisherLinköping University Electronic Press
ISBN (Print)978-91-7519-380-9
Publication statusPublished - 2014
Event10th International Modelica Conference - Lund, Sweden
Duration: 2014 Mar 102014 Mar 12

Publication series

ISSN (Print)1650-3686


Conference10th International Modelica Conference

Bibliographical note

project=LCCC-modeling, langopt, collocation

Subject classification (UKÄ)

  • Control Engineering


Dive into the research topics of 'Symbolic Transformations of Dynamic Optimization Problems'. Together they form a unique fingerprint.

Cite this