Reduction of lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations

Abstract

This article is devoted to the study of lower semicontinuous solutions of Hamilton-Jacobi equations with convex Hamiltonians in a gradient variable. Such Hamiltonians appear in the optimal control theory. We present a necessary and sufficient condition for a reduction of a Hamiltonian satisfying optimality conditions to the case when the Hamiltonian is positively homogeneous and also satisfies optimality conditions. It allows us to reduce some uniqueness problems of lower semicontinuous solutions to Barron-Jensen and Frankowska theorems. For Hamiltonians, which cannot be reduced in that way, we prove the new existence and uniqueness theorems.

References in corpus (5)

• Minimax and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations for Time-Delay Systems
• Representation of Hamilton-Jacobi equation in optimal control theory with compact control set
• An initial condition reconstruction in Hamilton-Jacobi equations
• Representation of Hamilton-Jacobi equation in optimal control theory with unbounded control set
• On nouniqueness of solutions of Hamilton-Jacobi-Bellman equations

Cited by in corpus (1)

• Stable representations of Hamilton-Jacobi-Bellman equations with infinite horizon