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A double-sided Dynamic Programming approach to the minimum time problem and its numerical approximation

Title data

Grüne, Lars ; Le, Thuy Thi Thien:
A double-sided Dynamic Programming approach to the minimum time problem and its numerical approximation.
In: Applied Numerical Mathematics. Vol. 121 (November 2017) . - pp. 68-81.
ISSN 1873-5460
DOI: https://doi.org/10.1016/j.apnum.2017.06.008

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PhD fellowship for foreign students at the Università di PadovaNo information

Abstract in another language

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: Article in a journal
Refereed: Yes
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)
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
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 04 Jul 2017 11:28
Last Modified: 14 Jul 2017 08:50
URI: https://eref.uni-bayreuth.de/id/eprint/38243

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