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Optimization-based subdivision algorithm for reachable sets

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Riedl, Wolfgang ; Baier, Robert ; Gerdts, Matthias:
Optimization-based subdivision algorithm for reachable sets.
In: Journal of Computational Dynamics. Bd. 8 (2021) Heft 1 . - S. 99-130.
ISSN 2158-2491
DOI: https://doi.org/10.3934/jcd.2021005

Dies ist die aktuelle Version des Eintrags.

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Projekttitel:
Offizieller Projekttitel
Projekt-ID
European Union's Seventh Framework Programme
338508

Projektfinanzierung: 7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union

Abstract

Reachable sets for nonlinear control systems can be computed via the use of solvers for optimal control problems. The paper presents a new improved variant which applies adaptive concepts similar to the framework of known subdivision techniques by Dellnitz/Hohmann. Using set properties of the nearest point projection, the convergence and rigorousness of the algorithm can be proved without the assumption of diffeomorphism on a nonlinear mapping. The adaptive method is demonstrated by two nonlinear academic examples and for a more complex robot model with box constraints for four states, two controls and five boundary conditions. In these examples adaptive and non-adaptive techniques as well as various discretization methods and optimization solvers are compared. The method also offers interesting features, like zooming into details of the reachable set, self-determination of the needed bounding box, easy parallelization and the use of different grid geometries. With the calculation of a 3d funnel in one of the examples, it is shown that the algorithm can also be used to approximate higher dimensional reachable sets and the resulting box collection may serve as a starting point for more sophisticated visualizations or algorithms.

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Publikationsform: Artikel in einer Zeitschrift
Begutachteter Beitrag: Ja
Zusätzliche Informationen: published Online First in October 2020, preprint appeared in December 2016

Contents:
1. Introduction and preliminaries
2. Grid construction via subdivision
3. Implementation
4. Numerical examples
5. Advantages of the algorithm
5.1 Transformed grids
5.2 Zooming
5.3 Determination of a bounding box
5.4 Parallelization
5.5 Solution funnel in 3d
6. Conclusions
Keywords: reachable sets; subdivision; optimal control; direct discretization; nonlinear
systems; nonlinear optimization
Fachklassifikationen: Mathematics Subject Classification Code: 93B03 49M37 (49M25 49J53 93C10)
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)
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Wissenschaftliches Rechnen
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: 23 Okt 2020 07:34
Letzte Änderung: 21 Mär 2022 10:00
URI: https://eref.uni-bayreuth.de/id/eprint/58682

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