Symbolic Transformations of Dynamic Optimization Problems

Fredrik Magnusson, Karl Berntorp, Björn Olofsson, Johan Åkesson

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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 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
Pages1027-1036
ISBN (Print)978-91-7519-380-9
Publication statusPublished - 2014
Event10th International Modelica Conference - Lund, Sweden
Duration: 2014 Mar 102014 Mar 12

Publication series

Name
Number96
Volume1650-3740
ISSN (Print)1650-3686

Conference

Conference10th International Modelica Conference
Country/TerritorySweden
CityLund
Period2014/03/102014/03/12

Bibliographical note

project=LCCC-modeling, langopt, collocation

Subject classification (UKÄ)

  • Control Engineering

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