Flocking with a moving leader for multiple uncertain lagrange systems

This paper addresses the flocking problem with a moving leader for multiple uncertain Lagrange systems under a proximity graph. Here a group of followers move cohesively with the moving leader to maintain connectivity, avoid collisions, and achieve velocity matching where the leader is a neighbor of only a portion of the followers and the followers interact with only their neighbors. Here in the proximity graph, the neighbor relationship is defined according to the relative distance between each pair of agents. We consider two cases: i) the leader moves with a constant velocity, and ii) the leader moves with a varying velocity. In the first case, a distributed continuous adaptive control algorithm accounting for unknown parameters is proposed in combination with a distributed continuous estimator for each follower. Here the relative position and relative velocity information between each follower and its neighbors are used in the control design. In the second case, a distributed discontinuous adaptive control algorithm and estimator are proposed. Here both the one-hop and two-hop neighbors´ information are used. In both cases, potential functions are used to preserve the connectivity as well as collision avoidance among the agents and the velocities of all followers converge to that of the moving leader asymptotically.