Cooperative Control via Congestion Game Approach

TL;DR

This paper presents a matrix-based congestion game approach for optimizing facility-based systems, enabling global optimization through individual agent payoff maximization and extending to systems with partial convertibility.

Contribution

It introduces a matrix formulation for congestion games, provides conditions for system convertibility into potential games, and extends the approach to nearly convertible systems.

Findings

System convertibility depends on facility-cost functions.

Global optimization achieved via agent payoff optimization.

Extension to systems with partial or near convertibility.

Abstract

The optimization of facility-based systems is considered. First, the congestion game is converted into a matrix form, so that the matrix approach is applicable. Then, a facility-based system with a system performance criterion is considered. A necessary and sufficient condition is given to assure that the system is convertible into a congestion game with the given system performance criterion as its potential function by designing proper facility-cost functions. Using this technology, for a dynamic facility-based system the global optimization may be reached when each agent optimizes its payoff functions. Finally, the approach is extended to those systems which are partly or nearly convertible.