Mitigating stop-and-go traffic congestion with operator learning

Abstract

This paper presents a novel neural operator learning framework for designing boundary control to mitigate stop-and-go congestion on freeways. The freeway traffic dynamics are described by second-order coupled hyperbolic partial differential equations (PDEs), i.e. the Aw–Rascle–Zhang (ARZ) macroscopic traffic flow model. The proposed framework learns feedback boundary control strategies from the closed-loop PDE solution using backstepping controllers, which are widely employed for boundary stabilization of PDE systems. The PDE backstepping control design is time-consuming and requires intensive depth of expertise, since it involves constructing and solving backstepping control kernels. Existing machine learning methods for solving PDE control problems, such as physics-informed neural networks (PINNs) and reinforcement learning (RL), face the challenge of retraining when PDE system parameters and initial conditions change. To address these challenges, we present neural operator (NO) learning schemes for the ARZ traffic system that not only ensure closed-loop stability robust to parameter and initial condition variations but also accelerate boundary controller computation. The first scheme embeds NO-approximated control gain kernels within a analytical state feedback backstepping controller, while the second one directly learns a boundary control law from functional mapping between model parameters to closed-loop PDE solution. The stability guarantee of the NO-approximated control laws is obtained using Lyapunov analysis. We further propose the physics-informed neural operator (PINO) to reduce the reliance on extensive training data. The performance of the NO schemes is evaluated by simulated and real traffic data, compared with the benchmark backstepping controller, a Proportional Integral (PI) controller, and a PINN-based controller. The NO-approximated methods achieve a computational speedup of approximately 300 times with only a 1% error trade-off compared to the backstepping controller, while outperforming the other two controllers in both accuracy and computational efficiency. The robustness of the NO schemes is validated using real traffic data, and tested across various initial traffic conditions and demand scenarios. The results show that neural operators can significantly expedite and simplify the process of obtaining controllers for traffic PDE systems with great potential application for traffic management.