Numerical and Symbolic Methods for Dynamic Optimization
Forskningsoutput: Avhandling › Doktorsavhandling (monografi)
Modelica is a standardized modeling language, which permeates the thesis. One of the many benefits of Modelica is that it is supported by several different tools, allowing implemented models to be used for different purposes. However, Modelica models are often developed for dynamic simulation and sometimes with little regard for numerics, which is enabled by the power of the available simulation software. Consequently, the models may be difficult to reuse for dynamic optimization, which is one of the challenges addressed by this thesis.
The application of direct collocation to DAE-constrained optimization problems is conventionally done by discretizing the full DAE. This often turns out to be inefficient, especially for DAEs originating from Modelica code. The thesis proposes various schemes to symbolically eliminate many of the algebraic variables in a preprocessing step before discretization to improve the efficiency of numerical methods for dynamic optimization, in particular direct collocation. These techniques are inspired by the causalization and tearing techniques often used when solving DAE initial-value problems in the Modelica community. Since sparsity is crucial for some dynamic optimization methods, we also propose a novel approach to preserving sparsity during this procedure.
A collection of five computationally challenging and industrially relevant optimal control problems is presented. The collection is used to evaluate the performance of the methods. We consider both computational time and probability of solving problems in a timely manner. We demonstrate that the proposed methods often are an order of magnitude faster than the standard way of discretizing the full DAE, and that they also increase probability of successful convergence significantly. It is also demonstrated that the methods are beneficial not only for DAEs originating from Modelica code, but also for more conventional textbook DAEs that have been developed specifically for optimization purposes.
|Enheter & grupper|
Ämnesklassifikation (UKÄ) – OBLIGATORISK
|Tilldelningsdatum||2016 nov 18|
|Status||Published - 2016 nov 18|
Fredrik Magnusson, Johan Åkesson, Anders Holmqvist, Karl Berntorp & Christian Andersson
2012/02/01 → 2017/02/01
Anders Holmqvist, Niklas Andersson, Anton Cervin, Anders Mannesson, Ather Gattami, Andrey Ghulchak, Alessandro Vittorio Papadopoulos, Anders Rantzer, Anders Robertsson, Aivar Sootla, ALFRED THEORIN, Bo Bernhardsson, Björn Olofsson, Björn Wittenmark, Christian Grussler, Charlotta Johnsson, Daria Madjidian, Erik Johannesson, Fredrik Magnusson, Fredrik Ståhl, Giacomo Como, Georgios Chasparis, Gabriel Turesson, Isolde Dressler, Johan Åkesson, Jang Ho Cho, Karl-Erik Årzén, Karl Johan Åström, Kin Cheong Sou, Karl Mårtensson, Karl Berntorp, Kristian Soltesz, Laurent Lessard, Martin Hast, Meike Rönn, Martin Ansbjerg Kjær, Martina Maggio, Maxim Kristalny, Olof Garpinger, Pål Johan From, Per-Ola Larsson, Pontus Giselsson, Rolf Johansson, Tore Hägglund, Vladimeros Vladimerou, Vanessa Romero Segovia, Andreas Aurelius, Gustav Cedersjö, Kaan Bür, Manfred Dellkrantz, Manxing Du, Payam Amani, Robin Larsson, William Tärneberg, Zheng Li, Lianhao Yin, Fredrik Tufvesson, Stefan Höst, Bernt Nilsson, Stig Stenström, Jens A Andersson, Stefan Diehl, Jonas Dürango, Mahdi Ghazaei Ardakani, Per-Ola Forsberg, Fredrik Bengtsson, Henrik Jörntell, Carmen Arévalo, Claus Führer, Christian Andersson, Fatemeh Mohammadi, Per Ödling, Mikael Andersson, Maria Kihl & Per Tunestål
2008/07/01 → 2018/06/30