Optimality principles and representation formulas for viscosity solutions of Hamilton-Jacobi equations. II. Equations of control problems with state constraints. (English) Zbl 1007.49016

Soravia, Pierpaolo

Differ. Integral Equ. 12, No. 2, 275-293 (1999).

Optimality principles for discontinuity super- and subsolutions of a Hamilton-Jacobi equation (HJE) with unbounded data are proved, although a comparison principle between super- and subsolution is not guaranteed. These general principles are then applied to control problems with target and state constraints. For a related mixed Dirichlet and constrained boundary problem to HJE for which the uniqueness fails in general, the minimal and maximal solutions are characterized as suitable value functions for the original control problem.
[See also Part I in Adv. Differ. Equ. 4, No. 4, 275-296 (1999; Zbl 0955.49016)].

Reviewer: Jiří Jarušek (Praha)

MSC:

49L25	Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
35F20	Nonlinear first-order PDEs
49L20	Dynamic programming in optimal control and differential games

Keywords:

controlled dynamic system; payoff; Hamilton-Jacobi equation; viscosity super and subsolutions; optimality principles; value function; state constraints; stability

Citations:

Zbl 0955.49016