Distributed Decision‐Making of General Linear Systems in Multi‐Coalition Games and Its Application to USV Swarm Confrontation

Abstract

This article explores a decision‐making problem with partial information in a multi‐coalition game that involves both cooperation and competition. Considering heterogeneous players with general linear systems, we propose a distributed algorithm that employs average consensus mechanisms to estimate the gradient of the coalition function among players within each coalition and utilizes leader‐following protocols to estimate the actions of all players across multiple coalitions. Furthermore, to reduce communication costs, a dynamic event‐triggered mechanism (ETM) is introduced into the average consensus and leader‐following protocols. The ETM is asynchronous, eliminating the requirement for a global clock and allowing players to transmit information only when the triggering condition is satisfied. By the Lyapunov analysis, all actions asymptotically converge to the Nash equilibrium by the proposed algorithms. Moreover, the unmanned surface vehicle (USV) swarm confrontation is formulated as a coalition game. In the scenario of safeguarding territorial integrity, we devise specific tasks for both the invading and defending USVs, encompassing elements such as formation, intrusion, defense, and so forth. The effectiveness of the proposed algorithms is validated through comprehensive simulations.