# Adaptive Cruise Control Based on Model Predictive Control with Constraints Softening
## 6 Conclusions  
A multi-target adaptive cruise control strategy based on the model predictive control algorithm is proposed in this paper. When applying the MPC to design the controller, various problems can arise, such as a weak robustness, the solution being unfeasible, and high computational complexity. The constraint softening method is adopted to improve the robustness and to avoid the solution becoming unfeasible because of the overlarge feedback correction. Utilizing the MPC framework is helpful to deal with multiple objectives for automotive applications. By introducing the error analysis of the weight matrix, MPC is constructed as a closed-loop system to improve the accuracy of the system solution.  
Simulations were conducted based on Matlab/Simulink and CarSim to verify the proposed ACC strategy in the FHWA Alt 3 Road condition. Two control strategies, ACC-Soften and MO-ACC, were compared to verify their performances in terms of car following, safety, comfort, and economy. The results indicate that the proposed ACC algorithm can improve the closed-loop convergence of MPC effectively and satisfy multiple control objectives. Constraint softening can be used to make the solution fall within the feasible region as far as possible. Compared with ACC-Soften, the variation range of acceleration with MO-ACC is larger. In this condition, the host vehicle needs to accelerate and decelerate more frequently, which results in discomfort of the passenger. Compared with MO-ACC, the proposed ACC-Soften control strategy shows a higher performance in terms of both comfort and economy when conducting safe car-following behavior.  
In future work, the proposed ACC strategy will be validated to include a comparison with other recent methods. Furthermore, the experimental parameters may influence the feasibility and effectiveness of the algorithm to a certain extent. The road surface coefficient will affect the driving torque and then affect the acceleration of the controller. The curvature radius of the road will also affect the acceleration of the host vehicle whilst tracking the road. In future work, experiments will be conducted to analyze these influence. We also plan to apply the proposed algorithm to a real vehicle and combine the driver brake optimization switch to develop a better ACC strategy.  
The main objectives in this paper focused on safety, car following, comfort, and economy, which were assessed under the framework of MPC. The proposed approach can serve as an upper controller to generate the desired acceleration, which can be applied to both electric vehicles and traditional vehicles with internal combustion engines to realize adaptive cruise control. The main purpose of this research was to enhance the active safety and intelligence of a distributed drive electric vehicle. Considering this application, in future, we hope to design a lower controller to distribute the desired torque for each wheel to achieve the desired acceleration.  
[PERSON] and [PERSON] conceived the idea of the study and conducted the research. [PERSON] analyzed most of the data and wrote the initial draft of the paper; [PERSON] and [PERSON] contributed to finalizing this paper. All authors have read and agree to the published version of the manuscript.  
Figure 4: Error of the inter-distance.  
**Funding:** This research was funded by the National Natural Science Foundation of China, grant number 51975089 and 51575079; the China Postdoctoral Science Foundation, grant number 2018M641688; the Scientific Research Fund from the Education Department of Liaoning Province, grant number IJYT201915.  
**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.