Abstract
In this paper, we are interested in how agents interact with each other in multi-agent systems. First, we model the interactions among agents in multi-agent systems as a multi-player game. The topology of the interactions among agents is a directed graph. We design cost functions for the game and assume that each agent in the systems tends to minimize its own cost. Then, the unique Nash equilibrium solution to the proposed multi-player game is obtained as the next state of the agent. A necessary and sufficient condition for achieving multi-agent consensus is established using the system transformation method and graph theory. Furthermore, we extend the result to the problem of containment control in the presence of leaders. The criterion for solving the containment control is also given in this paper. Finally, several simulation examples are given to verify the effectiveness of the theoretical results.
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