Distributed Formation-Containment Control for Discrete-Time Multiagent Systems Under Dynamic Event-Triggered Transmission Scheme

In this article, the distributed formation-containment (FC) control issue is investigated for a class of discrete-time multiagent systems (DT-MASs) under the event-triggered communication mechanism. In order to save the communication cost and improve the utilization of communication resources, a novel dynamic event-triggered (DET) mechanism is developed by adding an auxiliary variable for each agent system, which is able to dynamically adjust the triggering threshold. A distributed FC control scheme under the DET mechanism is proposed for all the leaders and followers based on the available relative outputs. The purpose of the addressed problem is to design the FC controller such that all the leaders achieve a formation shape and all the followers converge into such a convex hull. To this end, the considered DT-MASs are first decoupled into a diagonal form by resorting to the property of the Laplacian matrix as well as the inequality technique. Then, two sufficient conditions are established to ensure the desired FC performance. Furthermore, the corresponding FC controller parameters are obtained in terms of the solutions to two matrix inequalities which only depend on the maximum and minimum nonzero eigenvalues of the Laplacian matrix. Finally, an illustrative example is provided to verify the validity of the developed control scheme.