This technical note addresses the distributed time-varying formation-containment (FC) control problem for heterogeneous general linear multi-agent systems (MASs: the virtual leader, multi-leaders and followers) based on the output regulation framework from an observer viewpoint under the directed topology which contains a spanning tree. All agents can have different dynamics and different state dimensions. A new format of time-varying formation (TVF) shape is proposed. The multi-leaders are required to achieve the TVF with tracking the virtual leader whose output is only available to a subset of them, and only need to send the information of their designed observers and TVF shapes to their neighboring followers. A new class of distributed adaptive observer-based controllers is designed with the mild assumption that both leaders and followers are introspective (i.e., agents have knowledge of their own outputs). Compared with the existing works, one main contribution is that the controllers are fully distributed with the proposition of TVF shapes. The simulation to multi-vehicle systems is also provided to verify the effectiveness of theoretical results.

This article deals with the fully distributed pull-based event-triggered bipartite fixed-time output consensus problem of heterogeneous linear multiagent systems (HLMASs) with an active leader, whose information can be merely accessed by a small fraction of followers. First, a class of fully distributed fixed-time observers is proposed for each follower to estimate the leader’s system matrices, position, and control input under the signed communication topology, respectively. Then, based on the estimations of leader’s system matrices, two adaptive algorithms are given to solve the regulator equations. Furthermore, the fully distributed fixed-time observer-based controllers associated with state feedback and output feedback are, respectively, proposed by employing the pull-based event-triggered mechanism (ETM) where each agent merely updates controller at its own triggering instants. Correspondingly, some sufficient criteria and the rigorous proofs are provided to ensure the implementation of bipartite output consensus in fixed time by using the Lyapunov stability theory and fixed-time stability theory. Moreover, the strictly positive lower bounds of intervals between two adjacent event-triggered times are derived, which means the Zeno behavior is ruled out. Finally, numerical simulations are performed to demonstrate the theoretical analysis.