The solution infinite horizon noncooperative differential game with nonlinear dynamics without the Hamilton-Jacobi-Bellman equation

TL;DR

This paper introduces a novel method for solving infinite horizon noncooperative differential games with nonlinear dynamics, enabling direct construction of feedback controls without relying on Hamilton-Jacobi-Bellman equations.

Contribution

A new approach is proposed to directly construct feedback optimal controls and costs in differential games without using Hamilton-Jacobi-Bellman equations.

Findings

Allows direct construction of feedback controls

Applicable to nonlinear dynamics in differential games

Avoids solving complex HJB equations

Abstract

For a non-cooperative m-persons differential game, the value functions ofthe various players satisfy a system of Hamilton-Jacobi-Bellman equations.Nashequilibrium solutions in feedback form can be obtained by studying a related system of P.D.E's.A new approach, which is proposed in this paper allows one to construct the feedback optimal control and cost functions J_i(t,x),i=1,...,m directly,i.e.,without any reference to the corresponding Hamilton-Jacobi-Bellman equations.