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Approximation of reachable sets by direct solution methods of optimal control problems

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005542
URN to cite this document: urn:nbn:de:bvb:703-epub-5542-7

Title data

Baier, Robert ; Büskens, Christof ; Chahma, Ilyes Aïssa ; Gerdts, Matthias:
Approximation of reachable sets by direct solution methods of optimal control problems.
Bayreuth , 2004

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Abstract

A numerical method for the approximation of reachable sets of linear control systems is discussed. The method is based on the formulation of suitable optimal control problems with varying objective function, whose discretization by Runge-Kutta methods leads to finite-dimensional convex optimization problems. It turns out that the order of approximation for the reachable set depends on the particular choice of the Runge-Kutta method in combination with the selection strategy used for control approximation. For an inappropriate combination, the expected order of convergence cannot be achieved in general. The method is illustrated by two test examples using different Runge-Kutta methods and selection strategies, in which the run times are analysed, the order of convergence is estimated numerically and compared with theoretical results in similar areas.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): erschienen In:
Optimization Methods and Software. Bd. 22 (2007) Heft 3 . - S. 433-452
Keywords: Approximation of reachable sets; Discretization of optimal control problems; Direct solution methods; Set-valued Runge-Kutta methods; Order of convergence; Linear optimal control problems
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-5542-7
Date Deposited: 19 May 2021 05:55
Last Modified: 19 May 2021 05:55
URI: https://epub.uni-bayreuth.de/id/eprint/5542

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