In traffic signal control, flow-based (optimizing the overall flow) and pressure-based methods (equalizing and alleviating congestion) are commonly used but often considered separately. This study introduces a unified framework using Lyapunov control theory, defining specific Lyapunov functions respectively for these methods. We have found interesting results. For example, the well-recognized back-pressure method is equal to differential queue lengths weighted by intersection lane saturation flows. We further improve it by adding basic traffic flow theory. Rather than ensuring that the control system be stable, the system should be also capable of adaptive to various performance metrics. Building on insights from Lyapunov theory, this study designs a reward function for the Reinforcement Learning (RL)-based network signal control, whose agent is trained with Double Deep Q-Network (DDQN) for effective control over complex traffic networks. The proposed algorithm is compared with several traditional and RL-based methods under pure passenger car flow and heterogenous traffic flow including freight, respectively. The numerical tests demonstrate that the proposed method outperforms the alternative control methods across different traffic scenarios, covering corridor and general network situations each with varying traffic demands, in terms of the average network vehicle waiting time per vehicle.

翻译：在交通信号控制中，基于流量（优化整体流量）和基于压力（均衡和缓解拥堵）的方法虽然常用，但通常被分开考虑。本研究引入统一框架，采用李雅普诺夫控制理论，分别为这些方法定义了特定的李雅普诺夫函数。我们发现了有趣的结果。例如，广为人知的回压方法等价于由交叉口车道饱和流量加权的微分队列长度。我们进一步通过加入基本交通流理论对其进行改进。控制系统不仅要确保稳定，还应能自适应于各种性能指标。基于李雅普诺夫理论的洞见，本研究为基于强化学习（RL）的网络信号控制设计了一种奖励函数，其智能体采用双深度Q网络（DDQN）进行训练，以实现对复杂交通网络的有效控制。将所提算法与多种传统及基于RL的方法分别在纯乘用车流和包含货运的异质交通流下进行比较。数值测试表明，在涵盖通道和一般网络且各具不同交通需求的多种交通场景下，所提方法在平均每车网络等待时间方面均优于其他控制方法。