The value function of an asymptotic exit-time optimal control problem

Abstract

We consider a class of exit--time control problems for nonlinear systems with a nonnegative vanishing Lagrangian. In general, the associated PDE may have multiple solutions, and known regularity and stability properties do not hold. In this paper we obtain such properties and a uniqueness result under some explicit sufficient conditions. We briefly investigate also the infinite horizon problem.

References in corpus (1)

• Bounded-From-Below Solutions of the Hamilton-Jacobi Equation for Optimal Control Problems with Exit Times: Vanishing Lagrangians, Eikonal Equations, and Shape-From-Shading

Cited by in corpus (1)

• HJ inequalities involving Lie brackets and feedback stabilizability with cost regulation