## 5 Conclusions  
This paper presents a comparative analysis of two model predictive control strategies aimed at optimizing adaptive cruise control systems for enhanced fuel efficiency and passenger comfort while ensuring safe driving behavior, with their key difference being the formulation of their cost functions:  
Figure 6: Comparison of distance error, velocity, and acceleration profiles of ego equipped with fuel consumption MPC and DP controllers with lead along ARDC driving cycle, [0, 450 s] zoom.  
Figure 7: Comparison of velocity and acceleration profiles of ego equipped with fuel consumption MPC and DP controllers with lead along RD2 driving cycle, [0, 450 s] zoom.  
* One strategy explicitly incorporates a fuel consumption term;
* The other indirectly addresses fuel efficiency by focusing on acceleration smoothing.  
The two MPC strategies are also benchmarked against a dynamic programming controller. The results show that both MPC controllers yield comparable outcomes in terms of computational efficiency, making them suitable for real-time implementation. In terms of performance, the MPC\({}_{\text{FC}}\), which includes the explicit fuel consumption term, marginally outperforms the alternative strategy, though it operates with slightly slower computational speed. However, the performance improvements are minimal, calling into question the added complexity and effort required for implementing MPC\({}_{\text{FC}}\). Furthermore, despite both controllers having the same number of tunable parameters, the tuning process for MPC\({}_{\text{FC}}\) was more time-consuming. Additionally, the development of MPC\({}_{\text{FC}}\) involved several assumptions and approximations, such as maintaining a constant gear ratio over the prediction horizon and applying polynomial fitting to the fuel map, which may not always be readily available.  
In conclusion, while MPC\({}_{\text{FC}}\) achieved slight performance advantages, the demonstrated potential for both MPC strategies to reduce fuel consumption and improve passenger comfort makes them both promising candidates for future ACC systems. As the automotive industry progresses towards more sustainable and efficient mobility solutions, advanced control strategies like MPC will be crucial in achieving these objectives. Given the marginal differences in performance, a controller that is easier to tune and implement may prove more viable for commercial deployment. Nonetheless, further validation in more realistic simulation environments is essential to fully explore and refine this comparison. In future work, we plan to test the developed algorithms in a more complex simulation environment and with a higher modeling fidelity in order to properly capture the vehicle and powertrain dynamics as well as the interference due to traffic and unexpected maneuvers.  
Conceptualization, F.M. and A.B.; methodology, F.M. and A.B.; software, A.B.; formal analysis, F.M. and A.B.; investigation, A.B.; writing--original draft preparation, F.M. and A.B.; writing--review and editing, F.M. and D.A.M.; supervision, D.A.M. All authors have read and agreed to the published version of the manuscript. This research received no external funding.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.