## 5 Results of Simulation  
In order to validate the proposed closed-loop longitudinal control system, simulations were conducted using the software IPG TruckMaker 12.0.1--a high-fidelity simulation environment widely used to assess vehicle dynamics and driver assistance systems--and MATLAB and Simulink R2022b. The vehicle dynamics were modeled using Mercedes-Benz Antos, as provided by TruckMaker12. Table 1 lists the parameters of the longitudinal vehicle model. All parameters listed in Table 1 are based on the default specification of this TruckMaker model, which reflects the typical characteristics of a real-world heavy-duty vehicle. Table 1 lists the parameters of the longitudinal vehicle model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Value** & **Units** \\ \hline m & 18,200 & kg \\ \(A_{f}\) & 12.48 & m\({}^{2}\) \\ \(C_{r}\) & 0.4 & - \\ \(C_{d}\) & 0.7 & - \\ \(\tau\) & 0.5 & s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameters used in the vehicle model. Furthermore, the simulation environment (IPG TruckMaker12) incorporates detailed physical modeling of key powertrain components, such as engine torque response, gear shifting logic, braking dynamics, and driveline efficiency. These high-fidelity models ensure that actuator behaviors--including limitations and delays--are realistically reproduced, enabling reliable validation of the proposed control strategy under real-world conditions. For the validation of the control system, four test scenarios were defined based on vehicle mass--the baseline mass (18,200 kg), a 9100 kg load, and an 18,200 kg load--and headwinds. In each scenario, the vehicle experienced speed variations during operation. To evaluate the longitudinal speed-tracking performance of the HDV, a time-varying speed profile, ranging from 35 to 65 km/h, was defined, as shown in Figure 5. This speed profile was designed to evaluate the controller's responsiveness under dynamically changing commands and external conditions. The simulations were conducted on a straight road with inclines to assess the robustness of the control system. The road friction coefficient was set to 0.7, and the sampling time was 10 ms to ensure real-time performance. For the longitudinal control of the vehicle, model uncertainties were introduced through external disturbances--specifically, road slope and headwind. The road slope conditions are shown in Figures 6 and 7. This setup allows for the verification of the controller's effectiveness in responding to continuous speed variations in a dynamic environment with common disturbances such as road gradients, headwinds, and changes in vehicle mass. Moreover, each scenario exhibits clearly defined acceleration limits. Consequently, the proposed control system was used to evaluate the vehicle's stability and tracking performance across different scenarios. As noted in [31], the predictor dynamics should be faster than the reference dynamics. We consider the following parameters of predictor dynamics:  
\[A_{prd}=\alpha A_{p};\ P_{prd}=\alpha P, \tag{48}\]  
The control parameters for the longitudinal control system are outlined in Table 2. The initial feedback gain parameters \(k_{x,0}\), \(k_{r,0}\) were selected by referring to the optimal gain values obtained from a baseline LQR controller. This ensures that the MRAC framework starts from a reasonable baseline with desirable closed-loop dynamics. The learning rates, represented by the adaptation gains \(\Gamma_{x}\), \(\Gamma_{r}\), and \(\Gamma_{d}\), were chosen to ensure the boundedness of all closed-loop signals and to guarantee stable adaptation behavior under varying driving conditions and external disturbances. To ensure fair comparison between the proposed method and the conventional MRAC, the same values for the initial gains \(k_{x,0}\) and \(k_{r,0}\) and learning rates \(\Gamma_{x}\), \(\Gamma_{r}\), and \(\Gamma_{d}\) were applied in both control systems.