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Construction of the Minimum Time Function Via Reachable Sets of Linear Control Systems. Part 1: Error Estimates

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Baier, Robert ; Le, Thuy Thi Thien:
Construction of the Minimum Time Function Via Reachable Sets of Linear Control Systems. Part 1: Error Estimates.
University of Bayreuth, Germany; Università di Padova, Italy
Bayreuth ; Padova , 2015 . - 30 S.

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Projekttitel:
Offizieller ProjekttitelProjekt-ID
PhD fellowship for foreign students at the Università di PadovaOhne Angabe

Projektfinanzierung: Andere
Fondazione CARIPARO

Abstract

The first part of this paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In particular, in this paper the theoretical justification of the proposed approach is restricted to a class of linear control systems. The error estimate of the fully discrete reachable set is provided by employing the Hausdorff distance to the continuous-time reachable set. The detailed procedure solving the corresponding discrete set-valued problem is described. Under standard assumptions, by means of convex analysis and knowledge of the regularity of the true minimum time function, we estimate the error of its approximation. Numerical examples are included in the second part.

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Publikationsform: Preprint, Postprint, Working paper, Diskussionspapier
Begutachteter Beitrag: Ja
Zusätzliche Informationen: Contents:
1. Introduction
2. Preliminaries
3. Approximation of the minimum time function
3.1 Set-valued discretization methods
3.2 Implementation and error estimate of the reachable set approximation
3.3 Error estimate of the minimum time function
3.4 Convergence and reconstruction of discrete optimal trajectories

published in arXiv at December 2015
Keywords: minimum time function; reachable sets; linear control problems; set-valued Runge-Kutta methods
Fachklassifikationen: Mathematics Subject Classification Code: 49N60 93B03 (49N05 49M25 52A27)
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)
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: 11 Jan 2016 08:10
Letzte Änderung: 11 Jan 2016 08:10
URI: https://eref.uni-bayreuth.de/id/eprint/29585