Title data
Riedl, Wolfgang ; Baier, Robert ; Gerdts, Matthias:
Optimization-based subdivision algorithm for reachable sets.
In: Journal of Computational Dynamics.
Vol. 8
(2021)
Issue 1
.
- pp. 99-130.
ISSN 2158-2491
DOI: https://doi.org/10.3934/jcd.2021005
This is the latest version of this item.
Related URLs
Project information
Project title: |
Project's official title Project's id European Union's Seventh Framework Programme 338508 |
---|---|
Project financing: |
7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union |
Abstract in another language
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.
Further data
Item Type: | Article in a journal |
---|---|
Refereed: | Yes |
Additional notes: | 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 |
Subject classification: | Mathematics Subject Classification Code: 93B03 49M37 (49M25 49J53 93C10) |
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) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Scientific Computing Profile Fields Profile Fields > Advanced Fields Profile Fields > Advanced Fields > Nonlinear Dynamics Research Institutions > Central research institutes > Bayreuth Research Center for Modeling and Simulation - MODUS Research Institutions Research Institutions > Central research institutes |
Result of work at the UBT: | Yes |
DDC Subjects: | 500 Science > 510 Mathematics |
Date Deposited: | 23 Oct 2020 07:34 |
Last Modified: | 10 Mar 2025 06:23 |
URI: | https://eref.uni-bayreuth.de/id/eprint/58682 |
Available Versions of this Item
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Optimization-based subdivision algorithm for reachable sets. (deposited 04 Feb 2017 22:00)
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Optimization-based subdivision algorithm for reachable sets. (deposited 15 Sep 2020 06:45)
- Optimization-based subdivision algorithm for reachable sets. (deposited 23 Oct 2020 07:34) [Currently Displayed]
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Optimization-based subdivision algorithm for reachable sets. (deposited 15 Sep 2020 06:45)