Stable Representations of Hamilton–Jacobi–Bellman Equations with Infinite Horizon

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 Basco and Frankowska (Nonlinear Differ Equ Appl 26:1–24, 2019). Furthermore, we demonstrate that our representations are stable. The obtained results are illustrated with examples.