Uniqueness of lower semicontinuous viscosity solutions for the minimum time problem. (English) Zbl 0949.49020

Alvarez, Olivier; Koike, Shigeaki; Nakayama, Isao

SIAM J. Control Optimization 38, No. 2, 470-481 (2000).

A uniqueness result for lower semicontinuous viscosity solutions of the Bellman equation associated with the minimum time problem is presented. The boundary condition that accompanies the Bellman equation differs from previous ones used by O. Cârjá, F. Mignanego and G. Pieri [J. Optimization Theory Appl. 85, No. 3, 563-574 (1995; Zbl 0826.49020)] or P. R. Wolenski and Y. Zhuang [SIAM J. Control Optimization 36, No. 3, 1048-1072 (1998; Zbl 0930.49016)] and consists in some continuity assumption on the reachable part of the boundary.

Reviewer: O.Cârjá (Iaşi)

MSC:

49L25	Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
35F30	Boundary value problems for nonlinear first-order PDEs
49L20	Dynamic programming in optimal control and differential games

Keywords:

semicontinuous viscosity solutions; dynamic programming principle; minimum time problem

Citations:

Zbl 0930.49016; Zbl 0826.49020