## 4 Numerical Experiments  
In this section, we perform several numerical experiments to verify the effectiveness of the proposed control strategy for the platoon forming process and the optimization strategy after the formation of the platoon. The tool used in the experiments is based on the MATLAB2020, the computer processor used is the Intel Core [EMAIL_ADDRESS] GHz, the graphics card is the NVIDIA GeForce GTX 1050 Ti, the memory is 16 GB and the memory of the VRAM is 128 MB. In this section, three scenarios with different initial states (the spatial distribution and velocity of vehicles) are discussed. In order to make a reasonable comparison, we provide the same model parameter values according to our previous research [30]. The parameters are listed in Table 2.  
**Scenario I**: In this scenario, all the following vehicles are distributed in the left lane of the leading vehicle at the initial state and are controlled to gradually merge into the lane where the leading vehicle is located one by one by adjusting their own positions. The spatial distribution \(\left[X^{i},Y^{i}\right]\) and the velocity \(\left[v_{x}^{i},v_{y}^{i}\right]\) of each \(i\)-\(th\) CAV at the initial state were set as given in Equation (17). Note that we use positive and negative signs to distinguish the speed direction in the Y direction. The vehicle velocity is negative when turning right and positive when turning left. \[\left[ \begin{array}{cc}X^{0}&Y^{0}\\ X^{1}&Y^{1}\\ X^{2}&Y^{2}\\ X^{3}&Y^{3}\\ X^{4}&Y^{4}\\ X^{5}&Y^{5}\end{array} \right]=\left[ \begin{array}{cc}50&2\\ 40&8\\ 31&10\\ 20&8\\ 15&10\\ 0&11\end{array} \right]\left(m\right),\ \ \left[ \begin{array}{cc}v_{x}^{0}&v_{y}^{0}\\ v_{x}^{1}&v_{y}^{1}\\ v_{x}^{2}&v_{y}^{2}\\ v_{x}^{3}&v_{y}^{3}\\ v_{x}^{4}&v_{y}^{4}\\ v_{x}^{5}&v_{y}^{5}\end{array} \right]=\left[ \begin{array}{cc}6.0&0.0\\ 3.0&-1.15\\ 14.0&-2.15\\ 8.0&0.35\\ 9.0&-0.15\\ 9.5&-0.4\end{array} \right]\left(m/s\right). \tag{17}\]  
The elements \(X^{i}\) and \(Y^{i}\) represent the lateral and longitudinal position coordinates of the \(i\)-\(th\) CAV in spatial coordinates, respectively. Similarly, \(v_{x}^{i}\) and \(v_{y}^{i}\) represent the lateral and longitudinal velocities of the \(i\)-\(th\) CAV, respectively. Index \(i=0\) indicates the platoon leader and \(i=1,2,3\cdots\) indicates the following vehicle \(i\) according to the position of the vehicle. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Values** & **Parameter** & **Values** & **Parameter** & **Values** \\ \hline \(A_{1}\) & 2.00 & \(\lambda\) & 0.056 & \(a_{max}\) & 4.001 \\ \(A_{2}\) & 8.00 & \(\alpha\) & 0.029 & \(b_{max}\) & 3.00 \\ \(\sigma\) & 1.22 & \(\beta_{1}\) & \(-0.169\) & \(v_{0}^{(\alpha)}\) & 22.032 \\ \(\eta\) & 3.00 & \(\beta_{2}\Figure 5 depicts the trajectories of the CAVs during the platoon formation process. The gray vehicle is identified as the vehicle out of the communication range in the first step, and thus it will not participate in platoon formation. Then, the red vehicle is identified as the leading vehicle based on the longitudinal position of the vehicle at the initial moment at the second step. The other vehicles are controlled through Step 3 to form a platoon. From Figure 5, it can be found that the leading vehicle keeps driving in its own lane without any deviation, and the following vehicles are gradually merged into the lane where the leading vehicle is located one by one by adjusting their own positions. Note that Figure 5(a,b) present the changes in the lateral and longitudinal velocities of CAVs during the platoon formation process, respectively. Figure 5(a) shows that the lateral velocities of the following vehicles can converge to the desired velocity (the velocity of the leading vehicle) and become stable in the end.