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This paper investigates the formation-containment (FC) control issue for heterogeneous linear multi-agent systems (MASs) via distributed event-triggered control. The target for leaders is to form a time-varying formation (TVF) shape around a reference signal which is the virtual leader. To estimate the virtual leader's state, we devise an adaptive event-triggered observer for leaders. In that case, followers are required to converge to the convex combinations of the leaders' outputs. Similarly, another observer is designed for followers to estimate the state information of the convex hull. With the TVF shapes and local sampled information of the designed observers, two distributed event-based protocols are proposed for leaders and followers based on the output regulation framework. Continuous communications are not required for either control laws updating or triggering functions and it is proved that Zeno behaviour is strictly excluded for each agent. Finally, a simulation example is provided to demonstrate the practicability of the theoretical results.

Formation-containment control of heterogeneous linear multi-agent systems with adaptive event-triggered strategies