## 4 Numerical Simulations  
### Experiments Design and Parameter Settings  
In order to verify the feasibility and practicability of the proposed strategy, two typical preset lane change scenarios are selected to conduct the experiments. In order to intuitively evaluate the control effects of the proposed control strategy, we first compare the motion trajectory and control input diagrams of the proposed CLC control strategy and the combined CACC and sine function (CACC_Sine) control strategy. The latter also adopts the lane change longitudinal-lateral independent analysis. Then the statistical indicators of the difference between the actual and the expected motion states of the two control strategies are presented to validate the improvement effect of the proposed CLC control strategy for ensuring the stability of traffic flow in the target lane after changing lanes. The parameters of the proposed model are presented in Table 1. For the weighting parameters, we select different weight coefficients depending on the importance of different terms in the optimization problem to ensure that the final optimization results meet the control requirements. Specifically, in the tuning process, we first determine the weight coefficients of the spacing and speed tracking errors (i.e., \(\widetilde{e}x_{M}\), \(\widetilde{e}x_{A}\), \(\widetilde{e}\widetilde{v}_{M}\), and \(\widetilde{e}\widetilde{v}_{A}\)), and in this study, we consider that the spacing and speed tracking errors of the lane change vehicle M and the cooperative vehicle A are of the same importance, so we set these weight coefficients to the same value, i.e., \(\omega_{ex_{M}}\)= \(\omega_{ex_{A}}\)= \(\omega_{ev_{M}}\)= \(\omega_{ev_{A}}\). After determining the weight coefficients of the spacing and speed tracking errors, we keep them unchanged and then adjust the weight coefficients of the control accelerations (i.e., \(a_{M}\) and \(a_{A}\)) and control jerks(i.e., \(j_{M}\) and \(j_{A}\)). In this study, considering the driving comfort, the accelerations and jerks of the controlled vehicles M and A should be ensured to be as small as possible, so the weight coefficients of the control accelerations and jerks are chosen to be larger than those of the spacing and speed tracking errors in this study. In addition, during the experiment, we found that too large control accelerations weight coefficients will prolong the time for the controlled vehicles to reach the desired motion states, so the control accelerations weight coefficients are higher than the spacing and speed tracking errors weight coefficients and smaller than the jerks weight coefficients in this experiment, that is \(\omega_{ex_{M}}\) = \(\omega_{ex_{A}}\)= \(\omega_{ev_{M}}\) = \(\omega_{ev_{A}}\) < \(\omega_{a_{M}}\) = \(\omega_{j_{M}}\). In these two comparative experiments, the CACC model for the longitudinal movement of the lane change adopts the CACC car-following model with constant time headway proposed in [45]. The lateral movement is described by the sine function, which is the same as the proposed CLC control strategy. Please note that there is no cooperation between all the controlled CAVs in this comparative control strategy. Therefore, vehicles M and A keep track of vehicles C and B during the LC-O phase and do not track vehicles B and M until the LC-T phase, and it is considered that their preceding vehicles suddenly change from the LC-O stage to LC-T stage. The selection of lane-changing time has a great influence on the security of the actual lane change on the highway. The statistical analysis shows that a vehicle generally takes 3-5 s to complete the accelerated lane-changing process. The longer time the vehicle takes, the more dangerous is the process [46]. Therefore, the duration of lane-changing process in the sine function is set as 4 s.  
The simulations are conducted on a two-lane road segment developed in Python. Two representative lane-changing scenarios are selected.