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Title data
Riedl, Wolfgang ; Baier, Robert ; Gerdts, Matthias:
Optimization-based subdivision algorithm for reachable sets.
Mathematisches Institut, Universität Bayreuth, Institut für Mathematik und Rechneranwendung, Universität der Bundeswehr in Neubiberg/München
Bayreuth
,
2016
. - 33 S.
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Project information
| Project title: |
Project's official title Project's id European Union's Seventh Framework Programme 338508 |
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| Project financing: |
Andere |
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.
Further data
| Item Type: | Preprint, postprint |
|---|---|
| Additional notes (visible to public): | 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) |
| 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) 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 |
| Language: | English |
| Originates at UBT: | Yes |
| URN: | urn:nbn:de:bvb:703-epub-3157-8 |
| Date Deposited: | 30 Jan 2017 07:33 |
| Last Modified: | 20 Mar 2019 10:56 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/3157 |
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