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. Note to Practitioners - In dynamic and uncertain environments, such as those encountered by mobile robot teams or autonomous vehicle platoons, external disturbances, environmental occlusions, and limited communication bandwidth can significantly impair the performance of traditional formation control strategies. The existing formation control methods often rely on the strong assumption that at least one follower can access the complete state or output of the leader, which is rarely practical in real-world scenarios. To address this challenge, this paper proposes a novel observer-based TVOFT scheme that operates solely on incomplete output measurements of the leader. In addition, a hybrid triggering mechanism is introduced to enable intermittent communication among agents. This design not only avoids excessive transmissions but also guarantees a strictly positive MIET, thereby improving both communication efficiency and robustness under disturbances. Numerical simulations suggest that this approach is feasible but it has not been tested in production. Future work will focus on improving formation safety performance by extending the proposed observer-based formation control approach to MASs under attack.