Optimal Control Points Problem in Domination Game on Large Scale Multi-Agent Systems

Abstract

In this paper, we deal with large scale multi-agent consensus systems in which some agents are assumed to be weakly controlled with feedback and consider a domination game between several players. We assume that each player can choose a set of controlled agents and input signals to control the states of all the agents to its own desired reference state. The reference states of the players are assumed to be different from each other, therefore, a conflict occurs between the players. The problem for each player is to choose a set of controlled agents to dominate the whole system as possible and we call this as a domination game. To find the optimal set of the controlled agents is essentially a complex combination problem, however, in this paper, we show that the optimal set can be given by small calculations. This result provides a strategy to the players for the domination game and we discuss the relationship between the structure of networks and monopolistic/equally domination games.