Event-based leader-follower consensus for multiple Euler-Lagrange systems with parametric uncertainties

An adaptive, distributed, event-triggered controller is proposed in this paper to study the problem of leader-follower consensus for a directed network of Euler-Lagrange agents. We show that if each agent uses the proposed controller, the leader-follower consensus objective is globally asymptotically achieved if the directed network contains a directed spanning tree with the leader as the root node. We provide a trigger function to govern the event time; at each event time the controller is updated. In doing so, we also obtain an explicit lower bound on the time interval between events and thus we conclude that the proposed controller does not exhibit Zeno behavior. Simulations are provided which show the effectiveness of the proposed controller. Also shown in the simulations is the piecewise constant nature of the control law; this significantly reduces the number of updates required by each actuator, thereby saving energy resources.