The bilateral minimal time function. (English) Zbl 1112.49024

Nour, C.

J. Convex Anal. 13, No. 1, 61-80 (2006).

Summary: We study the minimal time function as a function of two variables (the initial and the terminal points). This function, called the “bilateral minimal time function”, plays a central role in the study of the Hamilton-Jacobi equation of minimal control in a domain which contains the target set, as shown in [F. H. Clarke and C. Nour, J. Convex Anal. 11, No. 2, 413–436 (2004; Zbl 1072.49018)]. We study the regularity of the function, and characterize it as the unique (viscosity) solution of partial Hamilton-Jacobi equations with certain boundary conditions.

MSC:

49L20	Dynamic programming in optimal control and differential games
49J53	Set-valued and variational analysis
49K24	Optimal control problems with differential inclusions (nec./ suff.) (MSC2000)
49K40	Sensitivity, stability, well-posedness

Keywords:

viscosity solutions; regularity of value functions; nonsmooth analysis; proximal analysis; Hamilton-Jacobi equations

Citations:

Zbl 1072.49018