## 4 Numerical Simulations
### Experiments Design and Parameter Settings
First, a general lane-changing scenario, where the longitudinal distance between vehicles B and A in the target lane is large enough to provide a safe lane-changing gap without requiring a significant speed adjustment by vehicle A. Second, the longitudinal distance between vehicles B and A in the target lane is relatively smaller, which requires vehicle A to make active speed adjustment to provide a safe lane change gap. The specific scene parameters at the beginning of the lane-changing process are presented below:  
Scenario 1: \(v_{M}(0)\) = 17 m/s, \(v_{B}(0)\) = 22 m/s, \(v_{C}(0)\) = 18 m/s, \(v_{A}(0)\) = 20 m/s, \(S_{CM}(0)\) = 18 m, \(S_{BM}(0)\) = 15 m, \(S_{MA}(0)\) = 22 m;  
Scenario 2: \(v_{M}(0)\) = 18 m/s, \(v_{B}(0)\) = 20 m/s, \(v_{C}(0)\) = 18 m/s, \(v_{A}(0)\) = 19 m/s, \(S_{CM}(0)\) = 10 m, \(S_{BM}(0)\) = 15 m, \(S_{MA}(0)\) = 10 m.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Related Parameters** & **Value** & **Related Parameters** & **Value** \\ \hline \(T\) & \(4\) s & \(d\) & \(3.5\) m \\ \(v_{\text{Omax}}\) & \(20\) m/s & \(v_{\text{Tmax}}\) & \(30\) m/s \\ \(d_{0}\) & \(5\) m & \(L_{1}\) & \(1\) \\ \(L_{2}\) & \(-1000\) & \(L_{3}\) & \(0.571\) \\ \(L_{4}\) & \(1\) & \(a_{We compare the control effects of the proposed model and the comparative model including the LC-O stage and LC-T stage, and select the same experimental duration, which is 30 s for scenarios 1 and 2. Performance Comparison of the Proposed CLC Control Strategy and Combination with CACC and Sine Function Control Strategy  
Figures 6 and 7 show the longitudinal position and speed variations of vehicles M, A, and B of two control strategies in scenario 1. Considering the longitudinal positions, as shown in Figure 6, the proposed CLC control strategy realizes smooth switching of vehicle A's tracking-preceding vehicles from vehicles B to M. It also makes the vehicles on the target lane (i.e., vehicles B, M, and A) quickly attain stable car-following states in the LC-T stage and keeps longitudinal safety distances among vehicles B, M, and A from the initial instant of the LC-T stage. As presented in Figure 6, for the comparative CACC_Sine control strategy, vehicle A in the LC-O stage regards vehicle B as its tracking-preceding vehicle. Therefore, in the LC-O stage, vehicle A gradually approaches vehicle B longitudinally in the LC-T stage, and vehicle A takes vehicle M as its new preceding vehicle. Eventually, during the transition from the LC-O stage to the LC-T stage, the longitudinal distance between the vehicles M and A is slightly higher as compared to the basic safety distance requirement, i.e., 5 m.  
Considering the longitudinal speeds, Figure 7 shows that the proposed CLC control strategy has smoother speed variation and less fluctuations as compared to the CACC_Sine control strategy. Furthermore, the proposed CLC control strategy considering the preceding vehicle switching avoids excessive speed adjustment in the LC-O stage, thus enabling a smooth speed transition from the LC-O stage to the LC-T stage (Figure 7a), instead of the more drastic speed change of the CACC_Sine strategy (Figure 7b). Moreover, the speed variation trends of the two control strategies show that the trajectory of vehicle A follows the trend of vehicle B from 5 s in the proposed CLC strategy, while in the CACC_Sine control strategy vehicle A follows from 10 s with an obvious sequential change. As an optimal controller, the proposed CLC control strategy obtains the optimal control quantities based  
Figure 6: The longitudinal positions of vehicles B, M, and A of the two control strategies in scenario 1. (**a**) The proposed CLC control strategy, (**b**) CACC_Sine control strategy. Figure 7: The longitudinal speeds of vehicles B, M and A of the two control strategies in scenario 1. (**a**) The proposed CLC control strategy, (**b**) CACC_Sine control strategy.