## 5 Conclusions  
An RL-based control method is proposed for CAVs at signalized intersections, aiming to optimize vehicle performance by holistically addressing energy consumption, traffic efficiency, driving comfort, and safety. The MDP framework for CAV driving is specifically tailored for multi-intersection environments, with the driving strategy trained by the TD3 algorithm. Furthermore, simulations of urban scenarios with multiple intersections are conducted to investigate the motion characteristics of the vehicle under various car-following modes. Results indicate that the proposed methods yield a 13.77% reduction in energy consumption and a notable 18.26% decrease in travel time. The findings reveal that this method allows the CAV to dynamically adjust to traffic conditions, improving travel efficiency and driving comfort, which can also lead to reduced fuel consumption.  
Since the simulation experiment reported in this paper is conducted under ideal conditions, within a scene devoid of random occurrences such as spontaneous overtaking or abrupt failures, the simulation is a valid testbed for the testing of algorithmic behavior. Notably, changes in factors such as traffic density, communication network reliability, and vehicle characteristics can lead to variations in simulation results. In practical use, considering the lack of perfect cooperation between CAVs and existing transportation infrastructure and the delay of communication systems, the actual optimization effect may require percentage correction, which will be scrutinized in a subsequent study.  
The primary research focus of this paper is to utilize RL algorithms to control a single agent, specifically addressing the longitudinal car-following behavior of an individual CAV. Due to the potential for the variance of the gradient to escalate with an increasing number of agents, it becomes imperative to devise and implement multi-agent RL algorithms. Moreover, reducing the dimensionality of the state space becomes essential, particularly for traffic scenarios featuring multiple CAVs. This represents one of the key research directions we aim to advance in the future. Future research will also focus on the lateral motion of CAVs on the road, combining lane-changing models to thoroughly study the driving behavior of vehicles. Moreover, a comprehensive analysis will be conducted from  
Figure 10: Variation of CAV acceleration with time in different car-following modes (0–150 s).  
the perspective of traffic flow to discuss the method under different CAV permeabilities, affording deeper insight into the proposed control strategy.  
Conceptualization, H.J., H.Z. and J.Z.; Data curation, Z.F. and Y.Q.; Formal analysis, H.J. and J.Z.; Funding acquisition, H.Z. and J.Z.; Investigation, Z.F.; Methodology, H.J.; Project administration, H.Z.; Resources, H.Z. and J.Z.; Software, H.J.; Supervision, H.Z. and J.Z.; Validation, H.J., Z.F. and J.Z.; Visualization, H.J.; Writing--original draft, H.J., Y.Q. and B.W.; Writing--review and editing, H.J. and B.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by National Key R&D Program of China (2021 YFB1600500), the Natural Science Foundation of Xizang Autonomous Region (XZ20201 ZR0040G), the Transportation Science and Technology Project of Sichuan Province (No. 2021-ZL-04), and the Science and technology project of Jiangsu transport (2023Y06).  
Not applicable.  
Data Availability StatementData in this study were produced through simulation experiments. Data sharing is not applicable to this article.  
The authors declare no conflict of interest.