Adaptive Event-Triggered Time-Varying Output Bipartite Formation Containment of Multiagent Systems Under Directed Graphs

The time-varying output bipartite formation containment (TVOBFC) problem for linear multiagent systems (MASs) under directed graphs is an important problem. However, the methods in existing works rely on the global information of the MASs or do not use event-triggered communication. This article investigates two kinds of TVOBFC problems for heterogeneous linear MASs under signed digraphs by event-triggered communication. For the first case where leaders have the same dynamics, the innovative fully distributed event-triggered protocol for the follower is proposed. In this case, the followers form the preset formation shape. For the second case where leaders have different dynamics, the leaders are divided into two groups. One group can directly obtain the output information of the virtual leader, while the other group cannot. In order to make leaders achieve the formation shape and track the virtual leader, two kinds of innovative observers are designed for two kinds of leaders to estimate the state of the virtual leader, and the control protocol is designed for each leader based on the designed observers. Then, the control law for each follower is designed to solve the formation containment problem. Finally, two examples are introduced to illustrate the main results.