# Dynamic Multi-Target Self-Organization Hunting Control of Multi-Agent Systems
## 5 Simulation Analysis  
This section provides the multi-target hunting simulation. In the simulation, the targets scatter in all directions, and the graph composed of all agents is not completely connected, but is connected at first. More importantly, the number of agents near some targets is less three, so we must initially finish the task allocation work before hunting begins. We can randomly generate three scattered escape targets and 12 agents in the area of X = [\(-\)1000 m,1000 m] and Y = [\(-\)1000 m,1000 m] to satisfy the above conditions. The detection distance is \(R_{\text{det}}=400\) m, and the collision avoidance distance is \(d_{\text{min}}=10\) m.  
A schematic diagram of the 12 agents and three targets at the initial moment is shown in Figure 2.  
In Figure 2, the red dot represents the agent, the green pentagram represents the target, the arrow direction represents the velocity direction, and the length of the arrow represents the speed. We can set the target to move at a constant speed of 3 m/s, according to the initial speed direction. The initial speed of the agent is 5 m/s, and the agents must change the speed in real-time, according to the assigned task situation, to ensure fast and efficient target hunting. Figure 2: Initial distribution map of the agent and target. The adjacency matrix is composed of 12 agents:  
\[a_{ij}=\left[ \begin{array}{ccccccccccccc}0&0&1&0&1&0&1&0&0&1&1&0\\ 0&0&0&0&0&1&0&0&0&0&0&1\\ 1&0&0&0&1&1&1&1&1&1&1\\ 0&0&0&0&1&0&0&0&0&1&0&0\\ 1&0&1&1&0&0&1&0&0&1&0&0\\ 0&1&1&0&0&0&1&1&1&1&1\\ 1&0&1&0&1&1&0&1&1&1&1\\ 0&0&1&0&0&1&1&0&1&1&1\\ 1&0&1&1&1&1&1&1&0&1&1\\ 1&0&1&0&0&1&1&1&1&0&1\\ 0&1&1&0&0&1&1&1&1&1&0\\ \end{array} \right]\]  
where 0 indicates no connection between the corresponding agents, and 1 indicates a connection relationship between the corresponding agents. The connection between the agents is shown in Figure 3. Figure 3 shows that the initial topology graph of the multi-agent systems is connected. Based on the information detected by the agent and the information obtained through communication with neighboring agents, the task assignment evaluation factor matrix is obtained through a fuzzy logic system:  
\[P_{ig}=\left[ \begin{array}{ccccccccccccc}0.81&0&0.41&0.09&0.29&0.16&0.51&0.2 &0.26&0.49&0.83&0.22\\ 0.38&0.8&0.75&0.8&0.77&0.81&0.43&0.47&0.57&0.73&0.52&0.78\\ 0.62&0.32&0.35&0.57&0.3&0.2&0.39&0.06&0.1&0.59&0.27&0.13\\ \end{array} \right]\]  
The parameters of the improved particle swarm optimization algorithm used in the distributed task allocation method are set as follows: the number of particles is 50, the number of iterations is 1000, the inertia weight is 0.8, and the learning factors are c1 = 2.0, c2 = 2.0. The optimal task allocation results are as follows:  
\[\text{optimal\_allocation}=\left[ \begin{array}{ccccccccccccc}1&2&3&4&5&6&7&8&9& 10&11&12\\ 1&2&3&3&2&2&1&2&2&3&1&2\\ \end{array} \right]\]  
where the first row indicates each of the 12 agents, and the second row indicates the serial number of the target assigned to each agent. Figure 3: The initial connection topology diagram, composed of 12 agents. The evaluation factor value for optimal fitness/optimal task allocation is 7.87. Figure 4 schematically shows the change curves of the number of iterations and optimal fitness/optimal task assignment evaluation factors. The relevant parameters for the hunting phase are set as follows: the step period is 0.25 s, and the number of iterations is 2000; meanwhile, \(K_{0}=0.8\), \(K_{1}=0.7\), and \(K_{2}=0.75\). Figures 5 and 6 show the position change process of the multi-agents. To intuitively understand the entire process of multi-agent hunting targets, Figure 5 shows the 2-D array diagrams of the changes in the positions of the agents and targets, respectively. The figures also display the real-time coordinate values of the targets, which further helps us observe the motion process. Figure 6 adds a time dimension and displays a 3-D array of changes in the positions of the agent and the target.