## 1 Introduction  
Optimizing traffic at intersections, a pivotal node within the urban road network and a critical hub for traffic flow regulation, is of paramount significance for the entire road network traffic system. Traditional vehicle driving faces significant constraints in terms of time and space, necessitating decisions within the confines of limited road space and transit time [1]. Conversely, the advent of Connected and Automated Vehicles (CAVs), spurred by advancements in connected vehicles and artificial intelligence, has revolutionized transportation. CAVs facilitate optimized driving behaviors via interactive learning with the surrounding environment [2, 3]. Within intelligent transportation systems, real-time adjustments to and optimizations of vehicle driving strategies at signalized intersections can be implemented based on detected vehicle trajectory data [4]. Traditional research often uses optimization models for single-objective or multi-objective goals focused on energy consumption and efficiency, aiming to solve for vehicle control parameters. In the realm of fuel vehicles, prior studies have mainly concentrated on enhancing fuel savings and minimizing emissions. Eco-driving strategies are developed through the integration of optimal control and trajectory optimization to minimize fuel consumption and enhance traffic efficiency. These strategies seamlessly incorporate real-time traffic prediction, vehicle connectivity, and signal control, all aimed at reducing fuel usage while ensuring smooth mobility [5, 6]. Utilizing optimal control techniques like mixed-integer linear programming and Pontryagin's minimum principle, models were devised to optimize vehicle trajectories and traffic signals, particularly at signalized intersections [7, 8]. Moreover, there is a concerted effort to merge offline planning with online tracking, fostering the development of energy-efficient driving strategies for CAVs. Simulation outcomes have underscored substantial gains in fuel efficiency alongside notable reductions in CO\({}_{2}\) emissions [9]. However, as electric vehicles emerge, research endeavors are gradually shifting towards achieving reduced power consumption. Current research focuses on enhancing the efficiency of hybrid electric vehicles (HEVs) and electric vehicles (EVs), particularly in autonomous driving. Such research integrates vehicle dynamics and powertrain optimization for better fuel economy. Methods like approximate dynamic programming and optimal control models have optimized fuel consumption in autonomous HEVs [10, 11]. Moreover, an analytical model determined optimal speed profiles for EVs, considering road and traffic conditions [12]. Additionally, an energy-efficient adaptive cruise control system was proposed for electric, connected, and autonomous vehicles (e-CAVs), improving energy efficiency compared to traditional strategies [13]. These efforts collectively advance the sustainability of HEVs and EVs in autonomous driving. Additionally, in the optimization of speed trajectories, researchers consider the temporal and spatial influences of vehicles at intersections. Depending on the driving mode, the vehicle speed is controlled in accordance with road characteristics and real-time traffic conditions. Dynamic eco-driving on main roads can yield up to 15% fuel savings and a reduction in carbon dioxide emissions [14]. A multi-objective speed planning model optimized electric vehicle trajectories, resulting in substantial electricity and time savings [15]. Additionally, an eco-driving method based on departure time prediction reduced delays at signalized intersections by optimizing CAV trajectories, showcasing notable efficiency improvements [16]. Furthermore, a novel car-following model considering road geometry enhanced traffic analysis and offered insights into stability and spatial separation contours [17]. However, the existing models are static, empirical, and designed for specific scenarios, relying on idealized assumptions.