## 6 MATLAB Simulation
### Scenario 2  
We introduce Scenario 2 in Figure 8. The distinctions of Figure 8 from Figure 4 are as follows. As the relative distance between the target and the ship is less than 3000 m, the target moves towards the ship directly while increasing its speed to 240 m/s. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**G** & \(\mathbf{N_{s}}\) & **cR** & **eD** & **sT** \\ \hline
3 & 1 & 100 & 95 & 57 \\ \hline
1 & 1 & 100 & 108 & 57 \\ \hline
3 & 10 & 100 & 94 & 57 \\ \hline
1 & 10 & 60 & 105 & 57 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: MC simulation results. The effect of changing system parameters, \(G\) and \(N_{s}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Control** & \(\mathbf{N_{s}}\) & **cR** & **eD** & **sT** \\ \hline \(PRO_{3}\) & 1 & 100 & 95 & 57 \\ \hline \(PRO_{1}\) & 1 & 100 & 108 & 57 \\ \hline \(PNG\) & 1 & 0 & 280 & 57 \\ \hline \(MCG\) & 1 & 0 & 280 & 57 \\ \hline \(CLOS\) & 1 & 20 & 276 & 56 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison with other state-of-the-art controls (Scenario 1). Figure 8 depicts the result of one MC simulation. We set \(G=5\) in Equation (4), i.e., we use \(G^{2}=25\) drones in total. The position of every drone at every 3 s is depicted as circles with distinct colors. A red asterisk depicts the position of the virtual agent at every 3 s. Figure 8 shows the case where the target is captured by a drone. Figure 9 is the enlarged figure of Figure 8. The position of every drone at every 3 s is depicted as circles with distinct colors. See that the grid formation is generated to protect the ship from the incoming target. Considering the scenario in Figure 9, Figure 10 removes the plots for the target's positions in order to see the drones' maneuvers clearly. The position of every drone at every 3 s is depicted as circles with distinct colors. A red asterisk depicts the position of the virtual agent at every 3 s. The position of the ship at every 3 s is indicated by red diamonds. A black asterisk presents the target's position when the target is hit by a drone. Figure 11 depicts the distance between the virtual agent and the target as time elapses. See that the relative distance continuously decreases over time. Figure 11 depicts the distance between the virtual agent and the ship as time elapses. See that the virtual agent stays close to the safety distance \(\beta\) while protecting the ship. Figure 11 depicts the side length as time elapses. As time elapses, the side length increases to \(\Delta\). Figure 8: The result of one MC simulation using the proposed grid formation. The position of every drone at every 3 s is depicted as circles with distinct colors. A red asterisk depicts the position of the virtual agent at every 3 s.  
Figure 10: Considering the scenario in Figure 9, we remove the plots for the target’s positions in order to see the drones’ maneuvers clearly. The position of every drone at every 3 s is depicted as circles with distinct colors. A red asterisk depicts the position of the virtual agent at every 3 s. The position of the ship at every 3 s is indicated by red diamonds. A black asterisk presents the target’s position when the target is hit by a drone. Figure 9: The enlarged figure of Figure 8. The position of every drone at every 3 s is depicted as circles with distinct colors. See that the grid formation is generated to protect the ship from the incoming target. Comparison with Other State-of-the-Art Guidance Laws (Scenario 2)  
Table 3 shows the MC comparison results of Scenario 2. In this table, \(N_{s}\) denotes the measurement noise. We run \(mC\) MC simulations per each control law. In Table 3, \(PRO_{q}\) indicates the proposed guidance law using \(G=q\) in (4). Note that only one drone is used in \(PRO_{1}\). Moreover, 25 drones are used in \(PRO_{5}\). Table 3 shows that the proposed control outperforms all other controls. \(MCG\), \(PNG\), and \(CLOS\) make a drone keep chasing the target.