# Adaptive Cruise Control for Cut-In Scenarios Based on Model Predictive Control Algorithm
## 5 Simulation Results and Analysis
### Cut-In within Safe Distance  
In driving scenario 3, there was a potential cut-in vehicle in a nearby lane and the relative distance between the host vehicle and the nearby vehicle did not satisfy the cut-in  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variables** & **Maximum** & **Minimum** & **Average** \\ \hline Acceleration (m/s\({}^{2}\)) & 0.3592 & \(-\)0.7310 & \(-\)0.0083 \\ jerk (m/s\({}^{3}\)) & 0.3357 & \(-\)0.5383 & \(-\)0.00052 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Statistics of the acceleration and jerk of the host vehicle under driving scenario 2.  
Figure 22: The simulation results of cut-in beyond a safe distance scenario: (**a**) the velocity of the host vehicle and the cut-in vehicle; (**b**) the relative distance between vehicles; (**c**) the acceleration of the host vehicle; and (**d**) the jerk of the host vehicle.  
vehicle safety distance model. Therefore, the vehicle needed to brake before the nearby vehicle cut in to provide a sufficient relative distance for the cut-in maneuver of the nearby vehicle, which avoided emergency braking of the vehicle, nervousness of the driver, reduction of driving comfort, and the risk of collision.  
In Figure 23, the cut-in vehicle performed a cut-in maneuver at a speed of 15 m/s at 26 s. Because the initial relative distance was 27 m, which did not satisfy the safety distance model of the cut-in vehicle, as shown in Figure 23a, before the nearby vehicle cut in at 26 s, with the cut-in possibility of the nearby vehicle increasing, the host vehicle recognized the cut-in intention of the nearby vehicle and started to slow down at 20 s. The host vehicle speed only decreased to 13.5 m/s which was higher than the minimum speed of the host vehicle without the cut-in recognition. As shown in Figure 23b, due to the early braking of the host vehicle, the relative distance between the host vehicle and the preceding vehicle increased to 43 m, which satisfied the safety distance model of the cut-in vehicle when the nearby vehicle performed the cut-in behavior at 26 s. At the same time, the following target of the host vehicle was smoothly switched to the cut-in vehicle; thus, the relative distance suddenly changed to 27 m, which is close to a stable relative following distance. After several seconds of adjustment, the host vehicle followed the cut-in vehicle steadily. Thus, the cut-in behavior of the nearby vehicle had little effect on the host car. In Figure 23, compared with the host vehicle without cut-in recognition, the vehicle with cut-in recognition obtained a smaller deceleration due to early braking, and prevented the rapid decrease in the relative distance caused by the sudden cut-in behavior of the nearby vehicle, which avoided emergency braking of the vehicle and driver nervousness. As shown in Figure 23c,d, the acceleration and jerk of the host vehicle with cut-in recognition had a smaller variation range, the maximum and minimum of acceleration and jerk of the host vehicle with cut-in recognition is smaller than that of the host vehicle without cut-in recognition, as shown in Tables 3