Stable Consensus Decision Making for Spatially Distributed Multiagent Systems with Multiple Leaders

This paper considers the consensus decision-making problem of spatially distributed multiagent systems with multiple leaders, where the leaders have the preference about the destination, while the followers have no such preference. The agents have limited capability to sense the movement information of their local neighbors determined via the spatial relative distance, and make movement decisions accordingly. The objective is to guide the followers to move with the same preferred direction as leaders have (i.e., reaching a stable consensus). We provide detailed analysis for the information transfer between the subgroups of leaders and followers, and establish quantitative results on the proportion of leaders needed to reach the stable consensus for two cases: leaders with the same preference and leaders with different preferences. For the system where the leaders have the same preference, we provide an upper bound (impossibility theorem) and a lower bound (sufficient condition) for the proportion of leaders needed in reaching the stable consensus. When the leaders have two different preferences, we provide a sufficient condition and a necessary condition on the proportions of two subgroups of leaders to achieve stable consensus decisions.