Optimal control with state-space constraint. I. (English) Zbl 0597.49023

Soner, Halil Mete

SIAM J. Control Optimization 24, 552-561 (1986).

The problem studied is the Hamilton-Jacobi-Bellman (HJB) equation associated to a deterministic optimal control problem with state space constraints. The principal results obtained are the following: 1) The optimal value function is the unique function that is a viscosity subsolution in the open domain, and a viscosity supersolution in the closed domain. 2) The optimal value function is bounded and uniformly continuous in the closed domain.

Reviewer: R.Gonzalez

MSC:

49L20	Dynamic programming in optimal control and differential games
35D99	Generalized solutions to partial differential equations
35J65	Nonlinear boundary value problems for linear elliptic equations
35K60	Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
60J60	Diffusion processes
93E20	Optimal stochastic control

Keywords:

Hamilton-Jacobi-Bellman (HJB) equation; deterministic optimal control problem; state space constraints; optimal value function; viscosity subsolution; viscosity supersolution