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Symbolic Transformations of Dynamic Optimization Problems

Magnusson, Fredrik LU ; Berntorp, Karl LU ; Olofsson, Björn LU and Åkesson, Johan LU (2014) 10th International Modelica Conference 1650-3740(96). p.1027-1036
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... (More)
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. (Less)
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author
; ; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Proceedings of the 10th International Modelica Conference
volume
1650-3740
issue
96
pages
1027 - 1036
publisher
Linköping University Electronic Press
conference name
10th International Modelica Conference
conference location
Lund, Sweden
conference dates
2014-03-10 - 2014-03-12
ISSN
1650-3686
ISBN
978-91-7519-380-9
project
LCCC
Numerical and Symbolic Algorithms for Dynamic Optimization
language
English
LU publication?
yes
additional info
project=LCCC-modeling, langopt, collocation
id
b19232b0-5f15-404a-a564-c1b3c9d03023 (old id 4222337)
date added to LUP
2016-04-04 14:22:31
date last changed
2019-12-09 15:01:29
@inproceedings{b19232b0-5f15-404a-a564-c1b3c9d03023,
  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.<br/><br>
<br/><br>
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.},
  author       = {Magnusson, Fredrik and Berntorp, Karl and Olofsson, Björn and Åkesson, Johan},
  booktitle    = {Proceedings of the 10th International Modelica Conference},
  isbn         = {978-91-7519-380-9},
  issn         = {1650-3686},
  language     = {eng},
  number       = {96},
  pages        = {1027--1036},
  publisher    = {Linköping University Electronic Press},
  title        = {Symbolic Transformations of Dynamic Optimization Problems},
  url          = {https://lup.lub.lu.se/search/ws/files/7670750/4253325.pdf},
  volume       = {1650-3740},
  year         = {2014},
}