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Baier, Robert ; Gerdts, Matthias ; Xausa, Ilaria:
Approximation of reachable sets using optimal control algorithms.
In: Numerical Algebra, Control and Optimization.
Bd. 3
(2013)
Heft 3
.
- S. 519-548.
ISSN 2155-3297
DOI: https://doi.org/10.3934/naco.2013.3.519
| Rez.: |
Dies ist die aktuelle Version des Eintrags.
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| Projekttitel: |
Offizieller Projekttitel Projekt-ID Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO) 264735-SADCO HIM Junior Trimester Program "Computational Mathematics", Research Group "Numerical discretization methods for differential inclusions and applications to robust optimal control problems" Group C |
|---|---|
| Projektfinanzierung: |
7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union Hausdorff Research Institute for Mathematics (HIM) in Bonn |
Abstract
We investigate and analyze a computational method for the approximation of reachable sets for nonlinear dynamic systems. The method uses grids to cover the region of interest and the distance function to the reachable set evaluated at grid points. A convergence analysis is provided and shows the convergence of three different types of discrete set approximations to the reachable set. The distance functions can be computed numerically by suitable optimal control problems in combination with direct discretization techniques which allows adaptive calculations of reachable sets. Several numerical examples with nonconvex reachable sets are presented.
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| Publikationsform: | Artikel in einer Zeitschrift |
|---|---|
| Begutachteter Beitrag: | Ja |
| Zusätzliche Informationen: | original version from April 2010, published as technical report in October 2011, updated in October 2012
Contents: 1. Introduction 2. Proximal Normals and Inner/Outer Approximation of Sets 2.1 Set Representation Techniques 2.3 Inner/Outer Approximation of Sets 3. Convergence Analysis 3.1 Properties and Approximations of Reachable Sets 3.2 Discrete Approximation of Reachable Sets 4. Numerical Realization 4.1 DFOG Method 5. Numerical Examples 5.1 Kenderov's Example 5.2 Bilinear Example 5.3 Adaptive Version 5.4 Example from a Pursuit-Evasion Game 6. Outline |
| Keywords: | reachable sets; optimal control; direct discretization |
| Fachklassifikationen: | Mathematics Subject Classification Code: 49J15 49M25 93B03 93C10 (90C30) |
| Institutionen der Universität: | Fakultäten Fakultäten > Fakultät für Mathematik, Physik und Informatik Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik) Profilfelder Profilfelder > Advanced Fields Profilfelder > Advanced Fields > Nichtlineare Dynamik |
| Titel an der UBT entstanden: | Ja |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 17 Apr 2015 08:36 |
| Letzte Änderung: | 27 Jun 2024 12:17 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/10420 |
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Approximation of reachable sets using optimal control algorithms. (deposited 11 Apr 2015 21:00)
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