Output Formation Tracking for Heterogeneous MASs With Incomplete Leader Measurements: A Hybrid-Triggering Observer Approach

This paper investigates the time-varying output formation tracking (TVOFT) problem for heterogeneous multi-agent systems (MASs) under the jointly observable condition (JOC). In practical applications, the neighboring followers of the leader often have access only to partial information due to external disturbances and occlusions, rendering existing formation control approaches ineffective. To address this challenge, we propose a set of distributed observers based on the JOC and a hybrid time-dynamic event-triggering mechanism (ETM) to estimate the leader’s state. Unlike standard ETMs, the triggering condition in the proposed hybrid triggering approach is evaluated only after a predetermined time interval, which serves as an explicit lower bound on the minimum inter-event time (MIET). This design ensures that the MIET remains positive. Theoretical analysis demonstrates that the proposed hybrid triggering approach effectively reduces redundant triggering actions while ensuring the robustness of communication performance against external disturbances. Building upon the developed distributed observer framework, we further propose a novel observer-based TVOFT scheme, which overcomes the conventional requirement that at least one follower must have full access to the leader’s state or output. Finally, numerical simulations are provided to validate the effectiveness of the proposed scheme.