Titlebar

Export bibliographic data
Literature by the same author
plus on the publication server
plus at Google Scholar

 

A new approach to the minimum time problem and its numerical approximation

URN to cite this document: urn:nbn:de:bvb:703-epub-1905-9

Title data

Grüne, Lars ; Le, Thuy Thi Thien:
A new approach to the minimum time problem and its numerical approximation.
Department of Mathematics, University of Bayreuth
Bayreuth , 2015 . - 17 S.

[img] PDF
Gruene_et_al_new_approach_min_time_prob_2015.pdf - Preprint
Available under License Deutsches Urheberrechtsgesetz .

Download (1MB)

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

We introduce a new formulation of the minimum time problem in which we employ the signed minimum time function positive outside of the target, negative in its interior and zero on its boundary. Under some standard assumptions, we prove the so called Bridge Dynamic Programming Principle (BDPP) which is a relation between the value functions defined on the complement of the target and in its interior. Then owing to BDPP, we obtain the error estimates of a semi-Lagrangian discretization of the resulting Hamilton-Jacobi-Bellman equation. In the end, we provide numerical tests and error comparisons which show that the new approach can lead to significantly reduced numerical errors.

Further data

Item Type: Preprint, postprint
Keywords: minimum time function; bridge dynamic programming principle; semi-Lagrangian discretization; error estimate; high order scheme.
Subject classification: Mathematics Subject Classification Code: 49L25 (49L20 65M12 65M15)
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 Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne)
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-1905-9
Date Deposited: 13 Mar 2015 09:36
Last Modified: 28 Mar 2019 11:11
URI: https://epub.uni-bayreuth.de/id/eprint/1905

Downloads

Downloads per month over past year