Uniqueness of lower semicontinuous viscosity solutions for the minimum time problem

Olivier Alvarez, Shigeaki Koike, Isao Nakayama

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We obtain the uniqueness of lower semicontinuous (LSC) viscosity solutions of the transformed minimum time problem assuming that they converge to zero on a `reachable' part of the target in appropriate direction. We present a counter-example which shows that the uniqueness does not hold without this convergence assumption. It was shown by Soravia that the uniqueness of LSC viscosity solutions having a `subsolution property' on the target holds. In order to verify this subsolution property, we show that the dynamic programming principle (DPP) holds inside for any LSC viscosity solutions. In order to obtain the DPP, we prepare appropriate approximate PDEs derived through Barles' inf-convolution and its variant.

Original languageEnglish
Pages (from-to)470-481
Number of pages12
JournalSIAM Journal on Control and Optimization
Volume38
Issue number2
DOIs
Publication statusPublished - 2000 Jan 1
Externally publishedYes

Fingerprint

Lower Semicontinuous
Viscosity Solutions
Dynamic Programming Principle
Subsolution
Uniqueness
Viscosity
Dynamic programming
Inf-convolution
Target
Convolution
Counterexample
Verify
Converge
Zero

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

Cite this

Uniqueness of lower semicontinuous viscosity solutions for the minimum time problem. / Alvarez, Olivier; Koike, Shigeaki; Nakayama, Isao.

In: SIAM Journal on Control and Optimization, Vol. 38, No. 2, 01.01.2000, p. 470-481.

Research output: Contribution to journalArticle

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