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Construction of the Minimum Time Function Via Reachable Sets of Linear Control Systems. Part 2: Numerical Computations

Title data

Baier, Robert ; Le, Thuy Thi Thien:
Construction of the Minimum Time Function Via Reachable Sets of Linear Control Systems. Part 2: Numerical Computations.
University of Bayreuth, Germany; Università di Padova, Italy
Bayreuth ; Padova , 2015 . - 16 p.

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Project information

Project title:
Project's official titleProject's id
PhD fellowship for foreign students at the Università di PadovaNo information

Project financing: Andere
Fondazione CARIPARO

Abstract in another language

In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other numerical approaches we provide a collection of numerical examples which either allow higher order of convergence with respect to time discretization or where the continuity of the minimum time function cannot be sufficiently granted, i.e. we study cases in which the minimum time function is Hölder continuous or even discontinuous.

Further data

Item Type: Preprint, postprint, working paper, discussion paper
Refereed: Yes
Additional notes: Contents:
1. Introduction
2. Numerical Tests
2.1 Linear examples
2.2 A nonlinear example
2.3 Non-strict expanding property of reachable sets
2.4 Problematic examples
3. Conclusions

published in arXiv at December 2015
Keywords: minimum time function; reachable sets; linear control problems; set-valued Runge-Kutta methods
Subject classification: Mathematics Subject Classification Code: 49N60 93B03 (49N05 49M25 52A27)
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)
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 11 Jan 2016 08:14
Last Modified: 25 Mar 2019 14:18
URI: https://eref.uni-bayreuth.de/id/eprint/29586