Game Theoretic Control of Multi-Agent Systems

TL;DR

This paper explores game-theoretic methods for controlling multi-agent systems, designing utility functions to ensure convergence to optimal system states under fixed and time-varying topologies.

Contribution

It provides necessary and sufficient conditions for utility function existence and introduces a novel control approach using potential games and Markov processes.

Findings

Utility functions can be designed using local information for convergence.

The system converges to Nash equilibrium or maximum system object.

A new control strategy guarantees convergence under dynamic topologies.

Abstract

Control of multi-agent systems via game theory is investigated. Assume a system level object is given, the utility functions for individual agents are designed to convert a multi-agent system into a potential game. First, for fixed topology, a necessary and sufficient condition is given to assure the existence of local information based utility functions. Then using local information the system can converge to a maximum point of the system object, which is a Nash equilibrium. It is also proved that a networked evolutionary potential game is a special case of this multi-agent system. Second, for time-varying topology, the state based potential game is utilized to design the optimal control. A strategy based Markov state transition process is proposed to assure the existence of state based potential function. As an extension of the fixed topology case, a necessary and sufficient condition for the existence of state depending utility functions using local information is also presented. It is also proved that using better reply with inertia strategy, the system converges to a maximum strategy of the state based system object, which is called the recurrent state equilibrium.