Differentiable Predictive Control for Large-Scale Urban Road Networks

TL;DR

This work addresses emissions-intensive urban traffic by reframing large-scale network control with Differentiable Predictive Control (DPC) applied to Network Macroscopic Fundamental Diagram (NMFD) models. By offline training of policy nets that approximate MPC-like objectives over differentiable NMFD/ANMFD dynamics, the approach achieves significant speedups and competitive or improved traffic performance compared to state-of-the-art Economic MPC. Key contributions include a constrained, differentiable policy architecture for perimeter control and routing guidance, extensive evaluation on scalability and robustness, and evidence that DPC scales favorably to networks with many regions while maintaining system constraints. The results imply substantial practical impact for real-time, energy-efficient urban traffic management and set the stage for online adaptation and data-parallel implementations in large city networks.

Abstract

Transportation is a major contributor to CO2 emissions, making it essential to optimize traffic networks to reduce energy-related emissions. This paper presents a novel approach to traffic network control using Differentiable Predictive Control (DPC), a physics-informed machine learning methodology. We base our model on the Macroscopic Fundamental Diagram (MFD) and the Networked Macroscopic Fundamental Diagram (NMFD), offering a simplified representation of citywide traffic networks. Our approach ensures compliance with system constraints by construction. In empirical comparisons with existing state-of-the-art Model Predictive Control (MPC) methods, our approach demonstrates a 4 order of magnitude reduction in computation time and an up to 37% improvement in traffic performance. Furthermore, we assess the robustness of our controller to scenario shifts and find that it adapts well to changes in traffic patterns. This work proposes more efficient traffic control methods, particularly in large-scale urban networks, and aims to mitigate emissions and alleviate congestion in the future.

Figures (8)

• Figure 1: Macroscopic Flow Diagram. This figure has $[\max g(x), \max g(x) \cdot 90\%$ highlighted in green, these are the optimal values of the MFD. The values of the MFD lower than $1$ with high accumulation are highlighted in red. This can be considered similar to a traffic jam.
• Figure 2: The figure shows the training and evaluation procedure. First, an initial condition is drawn from the dataset. This initial condition is provided to the model and policy. The policy generates a control input, which is provided to the model. The model generates a new state, noise is added, and this process is repeated for $N$ steps. At each step, the state and the control input are logged in the output. Our loss function is computed on the output and backpropagated to train the network. When evaluating, the policy and the plant model are evaluated in a closed-loop fashion.
• Figure 3: This figure shows the layout of the regions in the Economic MPC Scenario. There are seven regions here, and only adjacent regions are connected in the NMFD model.
• Figure 4: This figure shows the spawn matrix for the Economic MPC Scenario. These spawning rates for traffic describe the scenario's evolution over time.
• Figure 5: This figure shows the total accumulation of traffic in the system at each timestep. In the PC setting we can see that the DPC achieves lower peak accumulation, and lower overall accumulation. In the PCRG setting, we see that the MPC achieves lower peak accumulation, but fails to dissipate the traffic by the end of the scenario.