Time optimal consensus tracking with multiple leaders

This paper considers a multi-agent system with multiple leader agents. All the agents have bounded inputs. Any two agents can communicate only if they are within a fixed distance of each other. Leaders are special agents which generate trajectories autonomously based upon certain objectives. The follower agents must partition into groups such that agents in each group track exactly one leader. Given a particular partition and the resulting information exchange topology, every follower in each group must converge onto their leader's trajectory in min-max time. A special directed spanning tree is selected in each group. Each follower agent in this tree pursues its tail agent using a time-optimal feedback policy. These local feedback laws achieve global min-max time consensus tracking for any general information graph. Further, a decentralised algorithm is proposed to partition the agents so that consensus tracking for all the groups is accomplished in the shortest possible time.