Title data
Grüne, Lars ; Le, Thuy Thi Thien:
A doublesided Dynamic Programming approach to the minimum time problem and its numerical approximation.
In: Applied Numerical Mathematics.
Vol. 121
(November 2017)
.
 pp. 6881.
ISSN 18735460
DOI: https://doi.org/10.1016/j.apnum.2017.06.008
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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 semiLagrangian discretization of the resulting HamiltonJacobiBellman equation. In the end, we provide numerical tests and error comparisons which show that the new approach can lead to significantly reduced numerical errors.
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A new approach to the minimum time problem and its numerical approximation. (deposited 14 Mar 2015 22:00)
 A doublesided Dynamic Programming approach to the minimum time problem and its numerical approximation. (deposited 04 Jul 2017 11:28) [Currently Displayed]