## 4 Simulation Results  
The \(\mathcal{L}_{1}\) adaptive controller, DDS middleware and graph theory are implemented. The quadrotor model parameters selected as in Table 1[32].  
In addition, the controller parameters are selected as \(\gamma\) = 10\({}^{6}\), \(k_{p}\) = 10 and \(k_{d}\) = 10. The communication topology between the agents is shown in Figures 3 and 4 by considering a set of quality of service policies in Table 2 that need to be satisfied before the communication between the publishers and the subscribers.  
A couple of cases were considered in the containment control results:  
* **Containment of UAVs without parameters uncertain:** A comparison between the backstepping controller and the \(\mathcal{L}_{1}\) controller for the containment of multiple UAVs is illustrated in the figures from Figures 5-8. This presents how the group of five UAVs can formalize in specific topology inside their leaders in 2D space without uncertainty in the inertia matrix.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Properties** & **Symbol** & **Value/Unit** \\ \hline Mass & m & 0.52 kg \\ Gravity Acceleration & g & 9.8 m/s\({}^{2}\) \\ Drag’s Translational & \(k_{t}\) & 0.95 \\ Drag’s Rotational & \(k_{r}\) & 0.105 \\ Ratio of Drag \& Thrust & \(d\) & 7.5\(\times\) 10\({}^{-7}\) kg \(\cdot\) m\({}^{2}\) \\ Inertia of \(x\)-axis & \(I_{x}\) & 0.0069 kg \(\cdot\) m\({}^{2}\) \\ Inertia of \(y\)-axis & \(I_{y}\) & 0.0069 kg \(\cdot\) m\({}^{2}\) \\ Inertia of \(z\)-axis & \(I_{z}\) & 0.0129 kg \(\cdot\) m\({}^{2}\) \\ Arm Length & \(L\) & 0.205 m \\ Propeller Inertia & \(I_{R}\) & \(3.36\times 10^{-5}\) kg \(\cdot\) m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: The quadrotor model parameters.  
Figure 5: UAVs containment at the first position based on \(L_{1}\) adaptive control without parameters uncertain.  
Figure 6: Full map of UAVs containment based on \(L_{1}\) adaptive control without parameters uncertain.  
The two Figures 5 and 6 illustrate the containment control of multi-UAVs without uncertainty in the parameters (mass and UAV inertia matrix) based on L1 adaptive control. It can be seen that all the UAVs were constituted in a star topology inside the four red leaders. On the other hand, Figures 7 and 8 illustrate the containment control of multi-UAVs without uncertainty in the parameters based on backstepping control. It is clear that the same results were obtained with lower performance than the L1 adaptive control and that is shown in Figure 7. Exchanging the information between the UAVs and the leaders was done through the DDS middleware.  
Figure 8: Map of UAVs containment based on backstepping control without parameters uncertain.  
Figure 7: UAVs containment at the first position based on Backstepping control without parameters uncertain.  
Figure 10: Full map of UAVs containment based on \(L_{1}\) adaptive control with parameters uncertain.  
Figure 9: UAVs containment at the first position based on \(L_{1}\) adaptive control with parameters uncertain.  
Figures 9 and 10 show the containment control of multi-UAVs with uncertainty in the parameters (mass and UAV inertia matrix) based on L1 adaptive control. It can be seen that all the UAVs were constituted in a star topology inside the four red leaders. The system's performance was not affected by this large variation in the mass and UAV inertia matrix. On the other hand, Figures 11 and 12 illustrate the containment control of multi-UAVs with uncertainty in the parameters based on backstepping control. It can be seen that all the UAVs were not constituted in a star topology inside the four red leaders. The system's performance was affected by these large variations in the mass and UAV inertia matrix. As in the first scenario, the exchange of information between the UAVs and the leaders was achieved through the DDS middleware.  
Figure 11: UAVs containment at the first position based on backstepping control with parameters uncertain.  
Figure 12: Map of UAVs containment based on backstepping control with parameters uncertain.