Adaptive backstepping based consensus tracking of uncertain nonlinear systems with event-triggered communication

This paper investigates the consensus tracking problem for a class of uncertain high-order nonlinear systems with parametric uncertainties and event-triggered communication. Under a directed communication condition, a totally distributed adaptive backstepping based control scheme is presented. Specifically, a decentralized triggering condition is adopted in this paper such that continuous monitoring of neighboring states, as required in some existing results, can be avoided. Besides, to handle the non-differentiability problem of virtual controllers, which arises from the utilization of neighboring states collected only at the triggering instants, the virtual controllers in each recursive step are firstly designed with continuous communication. Then, the partial derivatives of these designed virtual controllers are adopted to construct distributed adaptive consensus controllers for the event based communication case. It is shown that with the presented distributed adaptive consensus control scheme and even-triggered communication mechanism, all the closed-loop signals are uniformly bounded and the output consensus tracking errors will converge to a compact set. Besides, the tracking performance in the mean square sense can be improved by appropriately adjusting design parameters.