On traveling wave solutions to Hamilton-Jacobi-Bellman equation with inequality constraints

TL;DR

This paper constructs and analyzes traveling wave solutions for Hamilton-Jacobi-Bellman equations with inequality constraints, revealing conditions for wave speed direction and behavior.

Contribution

It introduces a Riccati transformation approach to derive and study nonlinear PDE solutions with range bounds in optimal control problems.

Findings

Existence of monotone traveling wave solutions

Identification of parameter regions for positive or negative wave speeds

Analysis of wave solution properties under constraints

Abstract

The aim of this paper is to construct and analyze solutions to a class of Hamilton-Jacobi-Bellman equations with range bounds on the optimal response variable. Using the Riccati transformation we derive and analyze a fully nonlinear parabolic partial differential equation for the optimal response function. We construct monotone traveling wave solutions and identify parametric regions for which the traveling wave solution has a positive or negative wave speed.