Index-free assignment formation of networked multi-agent systems

This paper deals with an assignment formation problem, where a set of reference states are given but each of them is not preassigned to a specific agent. Thus, agents can achieve any reference states. We show that for the assignment formation the agents do not have to recognize their indexes. Then, we design an index-free controller with which this task is achieved the most approximately over a given network among all other index-free controllers. Finally, the effectiveness of the proposed method is demonstrated through numerical examples.