Scalable Formation Control for Second-Order Multiagent Systems: An Event-Triggered Predefined-Time Strategy

This article investigates the problem of distributed formation tracking control for second-order multiagent systems with unknown inertias. The leader-follower longitudinal formation control is considered and the target is to make followers achieve the same speed with the leader and maintain a desired longitudinal spacing. To make sure that the transient time is within user's preset time and the communication and computation resources are reduced, we focus on the event-triggered predefined-time control problem. To solve the problem, we design a node-based event-triggered controller in which coupling weights are updated based on an adaptive mechanism. Moreover, a state transformation is considered, and by analyzing the predefined-time stability of the transformed state, both the predefined-time longitudinal formation and the boundedness of controller are proved. Note that, with the adaptive updating mechanism, the control parameters do not depend on the information of Laplacian matrix and the bounds of unknown inertias. Thus, the formation is scalable for the case where some agents leave or join in the formation. Furthermore, to avoid updating the desired spacing manually when agents join or leave, we propose a fully distributed event-triggered predefined-time desired spacing decision algorithm based on distributed resource allocation algorithm. With the combination of the proposed spacing decision algorithm and controller, the longitudinal formation control is more scalable, time-saving and energy-saving.