## 5 Control Algorithms for UAV Networking
### Centralized Control Algorithm
#### 5.1.1 Leader-Follower  
The leader-follower method is one of the most popular control strategies applied in UAV swarm control. This method uses a hierarchical structure, in which one or several UAVs are designated as leaders, who are responsible for guiding the movement of the entire system. The remaining UAVs act as followers, maintaining their positions and distances relative to the leader UAV according to predetermined rules (as shown in Figure 26). This model reduces the complexity of swarm control by breaking down the coordination problem into simpler tasks. Each UAV only needs to focus on following the leader UAV or other UAVs in the formation. This makes the system stable, flexible, and easy to expand in actual deployment. Graph theory is applied in the leader-follower method to maintain the formation and ensure the performance of the UAV group. In this, each UAV is viewed as a vertex and the relationship between the leader and the follower is represented by a directed edge. In [79], the UAVs in the formation maintain a fixed distance between pairs of UAVs to ensure that the entire formation moves as a rigid block. Graph theory is used to determine the pairs of UAVs that need to maintain distance to preserve the formation shape. In addition, decentralized control laws are proposed to restore the shape when the distance between the UAVs is changed. A typical example studied is a group of three UAVs flying in an equilateral triangle formation, with the center of gravity moving along a certain trajectory while maintaining a stable velocity. In [80], graph theory is applied to quantitatively evaluate the effectiveness of UAV formations in performing missions. Performance criteria are analyzed for different UAV connectivity models, including fully connected, star, circular, tree, generally connected, mixed, and cellular networks. In [81], the scalability of a UAV formation control system is studied to maintain stability as the number of UAVs changes. A biologically inspired method, called the Veteran Rule, is proposed to ensure that the formation remains stable without re-adjusting the control parameters. The method also considers the fault tolerance of the system against unwanted connections, and it uses the Gershgorin Circle Theorem to set an upper bound on the strength of unwanted links. Figure 26: Two examples of controllers for followers. Figure 25: An example of a centralized control algorithm is a swarm of UAVs with a centralized ground control station. In some studies, quadratic sliding mode control (SMC) and quadratic linear regulation (LQR) are combined to control UAV formation. LQR is responsible for controlling the position in the outer ring, and SMC ensures stability and reduces errors in the inner ring, allowing the UAV to closely follow the leading UAV in both horizontal and vertical planes [82]. Another method uses SMC combined with adaptive PID control to handle communication delay, ensuring a stable UAV formation during flight, while reducing noise and state errors [83; 84]. In addition, to accurately track the trajectory of the leading UAV, a control method based on continuous quadratic sliding mode is developed, which helps the UAV to maintain a stable position and Euler angle by combining two-stage control [85]. Another study used the time-scale separation method between translational and rotational dynamics to control the UAV according to the leader-follower model, which helps the UAV track the trajectory smoothly and maintain a suitable distance [86]. For fixed-wing UAVs, a waypoint-based geometric control method is proposed to ensure that the UAVs can quickly converge into the desired formation. This method also integrates a speed adjustment mechanism to maintain the correct formation during flight and formation changes [87]. In addition, it uses an exponential disturbance observation model combined with adaptive backstepping control and approach speed-based glide control.