An initial condition reconstruction in Hamilton-Jacobi equations

TL;DR

This paper explores how to reconstruct initial conditions for Hamilton-Jacobi equations related to optimal control problems by solving the equations backward in time, aiding in understanding and solving such problems.

Contribution

It introduces a method to identify initial conditions for HJE associated with optimal control, enhancing the ability to analyze and solve these equations.

Findings

Reconstruction of initial conditions is feasible via backward solving.

Method improves understanding of solution behavior in optimal control.

Provides a framework for initial condition retrieval in HJE.

Abstract

We describe the family of initial conditions for Hamilton-Jacobi equations (HJE) corresponding to optimal control problems that can be retrieved by solving HJE backward in time.