On Data-based Nash Equilibria in LQ Nonzero-sum Differential Games

TL;DR

This paper develops data-driven methods for solving linear-quadratic nonzero-sum differential games, including deterministic and stochastic cases, and validates the approaches through numerical experiments.

Contribution

It introduces data-based solutions for LQ nonzero-sum differential games that are equivalent to traditional model-based methods, applicable in both deterministic and stochastic settings.

Findings

Data-based solutions match known model-based procedures.

Solutions are validated through numerical experiments.

Applicable to both deterministic and noisy measurement scenarios.

Abstract

This paper considers data-based solutions of linear-quadratic nonzero-sum differential games. Two cases are considered. First, the deterministic game is solved and Nash equilibrium strategies are obtained by using persistently excited data from the multiagent system. Then, a stochastic formulation of the game is considered, where each agent measures a different noisy output signal and state observers must be designed for each player. It is shown that the proposed data-based solutions of these games are equivalent to known model-based procedures. The resulting data-based solutions are validated in a numerical experiment.