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Approximation of reachable sets using optimal control algorithms

URN to cite this document: urn:nbn:de:bvb:703-epub-1980-4

Title data

Baier, Robert ; Gerdts, Matthias ; Xausa, Ilaria:
Approximation of reachable sets using optimal control algorithms.
Department of Mathematics, University of Bayreuth
Bayreuth , 2010 . - 46 S.

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Project information

Project title:
Project's official titleProject's 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

Project financing: 7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union
Hausdorff Research Institute for Mathematics (HIM) in Bonn

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): original version from April 2010, published as technical report in October 2011

Contents:

1. Problem Formulation
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
6. Outline
Keywords: reachable sets; differential inclusions; direct discretization of optimal control problems; distance functions; discrete approximations
Subject classification: Mathematics Subject Classification Code: 93B03 (49J15 49M25 34A60 65L06)
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-1980-4
Date Deposited: 27 Mar 2015 10:48
Last Modified: 27 Mar 2015 10:48
URI: https://epub.uni-bayreuth.de/id/eprint/1980

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