# Consensus Tracking Control of Multiple Unmanned Aerial Vehicles Subject to Distinct Unknown Delays
## 1 Introduction  
In recent years, the study of multiple unmanned aerial vehicles (UAVs) in formation has attracted attention, because of their diverse applications in target enclosure and tracking, search and rescue, surveillance, and heavy payload transportation, among others [1; 2; 3; 4]. Compared with a single UAV, as in [5], using multiple UAVs working cooperatively has advantages, such as greater thrust force, high efficiency, wide coverage area, and increased versatility. A multiple UAV system can be conceptualized as a multi-agent system (MAS). MAS formation and tracking control is considered a fundamental problem, in which agents are required to produce a desired trajectory. This topic has been extensively studied in the literature [6; 7; 8]. One of the most commonly proposed approaches for formation control in MASs is consensus protocols [9; 10; 11; 12]. Consensus means that a team of agents reaches an agreement about a particular variable of interest by interacting with each other via a communication network. Some studies [13; 14; 15; 16; 17; 18; 19; 20; 21] suggested that consensus protocols in multi-agent systems provide benefits such as achieving agreement in various conditions(antagonistic interactions, noisy environments, and heterogeneous systems), enabling distributed and adaptive solutions, and ensuring stability and finite settling times. Consensus protocols can be affected by the presence of time-varying delays, which can lead to reduced performance, instability, or prevent the desired agreement. Certain protocol designs can compensate for these delays, ensuring proper system performance and achieving consensus under specific conditions such as network topologies [23; 24] and design parameters [25]. Other authors have explored different approaches, such as consensus protocols based on observation. For example, the authors in [26; 27] addressed this problem by designing a leader-follower consensus control strategy based on predictive control, where an observer is used for estimation of the state of the agents when communication constraints exist. The authors in [28] presented a predictive extended state observer (ESO) to estimate the consensus tracking error when having time-varying input/output delays and mismatched disturbances in a linear MAS, and the ESO was used for designing the controller. In addition, ref. [29] developed a distributed extended state observer and a leader-follower consensus control based on the relative estimated states between each agent and its neighbors in the presence of unknown external disturbances. Moreover, the authors in [30; 31] focused on the problem of fault detection for a MAS in continuous time, where they used consensus protocols and unknown input observer (UIO) schemes to deal with disturbances, failures, and time-varying delays, a where numerical example demonstrated the effectiveness and feasibility of the proposed approach. The authors in [32] implemented a fault diagnosis strategy based on the stages of detection, isolation, and estimation for satellites in formation. In the isolation stage, a bank of robust and non-linear UIOs were designed to isolate the faulty actuator, allowing the unknown input disturbances to be decoupled and their effects attenuated. In addition, UIOs can effectively track state errors in multi-agent systems with directed switching topologies, enabling consensus tracking, even with external inputs affecting the leader [33]. For example, the authors in [34] used a UIO to estimate an unknown state affected by simultaneous connectivity-mixed attacks, actuator/sensor faults, and disturbances, and developed a leader-follower consensus control for a MAS. In summary, research indicates that consensus in multi-agent systems can be achieved despite unknown input delays or faults. Protocols that utilize UIOs to detect, isolate, or estimate these elements have been developed, ensuring that the systems can reach consensus. In general, time-varying delays are unavoidable in complex systems such as UAVs.