# Path Tracking Control Strategy Based on Adaptive MPC for Intelligent Vehicles
## 5 Simulation Verification
This enhances both path tracking accuracy and vehicle stability. Set the road adhesion coefficient as 0.3 and the initial vehicle speed as 30 km/h. The simulation results are shown in Figure 11.  
Figure 11: Simulation results of \(\mu=0.3\) variable curvature. (**a**) Path tracking trajectories; (**b**) Lateral tracking deviation; (**c**) Yaw angle stability; (**d**) Yaw rate constraints. In the path tracking trajectory (Figure 11a), the MPC controller exhibits a maximum lateral deviation of 0.5 m, with noticeable vehicle slip occurring at curve exits. The HOSMC controller reduces the deviation to 0.25 m but introduces significant trajectory jitter (slip ratio > 10%). In contrast, the conditional adaptive controller maintains stable tracking within 0.15 m deviation and completely avoids slip phenomena. For lateral tracking deviation (Figure 11b), the MPC shows a peak deviation of 0.48 m and requires an extended recovery time (2 s). The HOSMC achieves a lower peak deviation (0.22 m) but suffers from persistent oscillations (\(\pm\)0.05 m). The conditional adaptive controller outperforms both, limiting peak deviation to 0.12 m with zero oscillations and a rapid 1 s recovery. Figure 13 presents a comparative analysis of the tracking path, yaw angle and yaw rate of the model under both the HIL test platform and the co-simulation platform. The findings indicate that, under the conditions involving variable curvature curves, the HIL test results align closely with those obtained from the CarSim/Simulink co-simulation. While the lateral and directional deviations observed in the HIL test under variable curvature conditions are marginally greater than those in the co-simulation, they still meet the tracking accuracy requirements of the controller. Figure 12: Diagram of HIL test platform. Figure 13: Comparison of HIL test results under variable curvature curve conditions. **(a)** Path tracking trajectories; **(b)** Yaw angle stability; **(c)** Yaw rate constraints. The HIL test demonstrates robust real-time performance, with an average processing latency of 5.2 ms per control cycle, well within the 10 ms threshold required for real-time operation. The system achieves a consistent update rate of 200 Hz, ensuring timely response to dynamic changes in curvature and steering maneuvers. Despite hardware-induced delays and noise interference, the maximum observed latency during large curvature transitions was 8.7 ms, which does not compromise the controller's stability or tracking precision. Additionally, the variation in the yaw rate during the HIL test is largely consistent with that in the co-simulation. Although the error in the HIL test slightly increases during large curvature steering maneuvers, it remains within an acceptable range. This discrepancy can be attributed to the system delays and noise interference inherent in the HIL simulation test hardware equipment, which contribute to a slightly larger error compared to the co-simulation. Nonetheless, the overall trend of various dynamic parameters remains consistent. These results affirm that the condition-adaptive MPC control model proposed in this paper is both feasible and effective in the actual controller operating environments, demonstrating high real-time performance and meeting the requirements for real vehicle applications.