On the Upper Bound of Near Potential Differential Games

TL;DR

This paper introduces a new upper bound for the distance between Linear Quadratic Near Potential Differential Games and exact potential differential games, linking this distance to trajectory errors and enhancing understanding of their dynamic similarities.

Contribution

It provides the first explicit upper bound for the distance in LQ NPDGs and establishes a linear relation between this distance and trajectory errors, facilitating future applications.

Findings

Established a novel upper bound for LQ NPDGs.

Linked the distance to trajectory errors linearly.

Enhanced understanding of the dynamic proximity in potential differential games.

Abstract

This letter presents an extended analysis and a novel upper bound of the subclass of Linear Quadratic Near Potential Differential Games (LQ NPDG). LQ NPDGs are a subclass of potential differential games, for which a distance between an LQ exact potential differential game and the LQ NPDG. LQ NPDGs exhibit a unique characteristic: the smaller the distance from an LQ exact potential differential game, the closer their dynamic trajectories. This letter introduces a novel upper bound for this distance. Moreover, a linear relation between this distance and the resulting trajectory errors is established, opening the possibility for further application of LQ NPDGs.