# Consensus Tracking Control of Multiple Unmanned Aerial Vehicles Subject to Distinct Unknown Delays
## 1 Introduction
Time-varying delays in UAVs are primarily caused by factors related to communication and computation, such as wireless communication issues, satellite communication transport delays, or problems with vision-based navigation systems. In UAV systems, time-delays can reduce the effectiveness of control performance, affecting the stability and making the system vulnerable to an actuator, sensor, or process fault. These problems become more critical in multiple-UAV systems in formation schemes. Therefore, developing formation control schemes for multiple UAVs subject to delays has attracted the attention of academia and industry. For example, the authors of [35] investigated the robust control problem of time-varying formation flight for multiple-UAV systems with external disturbances and time delay. However, ref. [35] only considered a model based on fixed-wing vehicles. Moreover, the authors in [36] proposed an algorithm for leader-following consensus control of multiple fixed-wing UAVs with time-varying delays and unknown external disturbances but limited their study to the dynamic model of the attitude (aircraft orientation). The time-varying delay problem for a single quadrotor was addressed in [37], where a Lyapunov barrier was used to ensure that the tracking error was limited within a range, and a Pade approximation was applied to compensate for the effect of input delay. In the literature, many works have addressed the problem of observer-based consensus formation control for different cases of multi-agent systems with time-varying delay. However, few studies have addressed this problem in the specific case of multi-UAV systems. Therefore, the main contribution of this work is a new methodology to obtain mitigation of an unknown input delay in a tracking control in the formation of multiple-UAV systemsunder consensus protocols, where the stability of the proposed scheme is proved in the leader and followers, despite unknown time-varying delays. It is essential to mention that unknown delays are assumed to be upper-bounded, and these bounds are not required to be known. In addition, the proposed observer-based control scheme guarantees the consensus tracking of multi-UAV systems with the desired \(H_{\infty}\) performance, which adds a further level of mitigation to unknown delays present in an MAS system by minimizing the \(H_{\infty}\) norm, which measures the maximum gain from the disturbance to the controlled output of the system. In other words, in the proposed method, we address the problem related to a distinct unknown delay of the input of cooperative control, where consensus tracking control for the translation dynamics based on an unknown input observer is proposed. Thus, the designed consensus control between the leader and followers is guaranteed, and this scheme can be applied to solve the cooperative control problem of multiple UAVs in the presence of distinct unknown delays. The paper is organized as follows. Section 2 is related to the dynamic model of the considered quadrotors and the problem formulation. Section 3 is dedicated to the control strategy design, which involves the inner attitude control and the consensus tracking control for translation. Section 3 analyzes the observer-based control strategy for the tracking control of the leader and follower agents, which involves observers used to isolate the unknown time-varying delays in the state estimation process; in addition, in this section, consensus tracking control under unknown time-varying delays is presented. Section 4 presents the results of numerical simulations, to show the effectiveness of the observer-based consensus control applied to multiple UAVs subject to distinct unknown time-varying delays. Finally, Section 5 ends the document with the conclusions.