Optimality of consensus protocols for multi-agent systems with interaction

This paper deals with consensus protocols for multi-agent systems with interaction. Each agent is driven by distributed control for achieving consensus, while it is simultaneously influenced by distributed disturbance for disturbing consensus. That is, two kinds of interconnections are considered, where the interconnections are assumed to be described as undirected graphs possibly different. A necessary and sufficient condition is stated for consensus achievement. A sufficient condition for optimality of the consensus is then presented as the key result of this paper, where it is shown that the distributed feedback can minimize a quadratic performance index under this condition. These two conditions are further investigated, and the graph topology desirable for consensus achievement is established from the viewpoint of inverse optimality.