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

TL;DR

This paper develops a stable, regular representation for infinite horizon Hamilton-Jacobi-Bellman equations with state constraints, simplifying the analysis of solutions and demonstrating robustness through examples.

Contribution

It introduces a new regular representation for these equations, enabling easier proof of existence, uniqueness, and stability of solutions.

Findings

Representation is stable under perturbations.

Simplifies proof of existence and uniqueness.

Illustrated with practical examples.

Abstract

In this paper, for the Hamilton-Jacobi-Bellman equation with an infinite horizon and state constraints, we construct a suitably regular representation. This allows us to reduce the problem of existence and uniqueness of solutions to the Frankowska and Basco theorem from (2019). Furthermore, we demonstrate that our representations are stable. The obtained results are illustrated with examples.