Leader selection via LASSO for formation control of time-delayed multi-agent systems

In this paper, we address a formation control problem with velocity assignment of networked multi-agent systems with heterogeneous time-delays. We assume the situation that the assigned velocity is transmitted as a command signal from human operators via long-range communication. For the cost reduction, only a part of the agents, called leaders, can receive this signal. First, we show that heterogeneous time-delays cause a formation error, and derive the error in an analytic way. Second, we propose a leader selection algorithm to minimize the formation error. Here, a small number of leaders is better from the viewpoint of the cost reduction. To meet this request, we employ the LASSO (least absolute shrinkage and selection operator) which has a function of selecting as few explanatory variables as possible in optimization problems. We focus on this function of the LASSO, and consider applying it to the leader selection problem. The effectiveness of the proposed method is verified by a numerical example.