Neural operators for adaptive control of freeway traffic

Lv, Kaijing; Wang, Junmin; Zhang, Yihuai; Yu, Huan · 2025 · Automatica

DOI: 10.1016/j.automatica.2025.112553

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Summary

This paper addresses the challenge of real-time adaptive control for freeway traffic, specifically targeting stop-and-go congestion caused by uncertain driver behaviors. The traffic dynamics are modeled using the Aw-Rascle-Zhang (ARZ) partial differential equation (PDE), a 2×2 hyperbolic system where the relaxation time—a critical parameter representing driver reaction delays—is unknown and spatially varying. Traditional adaptive control methods for such PDEs rely on backstepping techniques that require solving complex kernel equations online at every time step as parameters are estimated. This process is computationally intensive, hindering real-time application. To overcome this, the authors propose a neural operator (NO) based approach that learns the mapping from system parameters to backstepping kernel functions, thereby accelerating the control computation. The methodology integrates DeepONet, a deep neural network designed for approximating operators, into an adaptive boundary control framework. Unlike previous works that approximated kernels for scalar PDEs, this study extends the framework to coupled 2×2 hyperbolic systems. The approach involves a passive identifier design to estimate unknown in-domain coefficients and boundary parameters. Instead of solving the Goursat-form PDE kernel equations online, a DeepONet is trained to approximate the exact gain operator, mapping estimated parameters to the corresponding kernel functions. The authors rigorously establish the stability of the system using Lyapunov analysis, proving that the controller employing DeepONet-approximated kernels ensures global stability. The theoretical framework is validated through numerical simulations comparing the proposed method against traditional PDE solvers and reinforcement learning (RL) approaches. The results demonstrate that the DeepONet-based approach is nearly two orders of magnitude faster than traditional PDE solvers for generating kernel functions, while maintaining an approximation loss on the order of $10^{-3}$. The study confirms that the neural operator can accurately learn the mapping for the entire family of system parameters rather than just single instances. Comparative experiments with reinforcement learning highlight that the proposed method does not rely on specific initial values and provides a model-based solution with guaranteed stability, whereas RL methods may suffer from performance degradation or instability when encountering initial conditions outside their training range. The stability proofs ensure that the system states converge to equilibrium despite the use of approximate kernels. The significance of this work lies in its demonstration that operator learning can effectively replace computationally heavy online PDE solving in adaptive control schemes. By applying DeepONet to the ARZ traffic model, the authors provide a scalable solution for real-time traffic management that handles uncertainty in driver behavior. This is the first application of this specific operator learning framework to the adaptive control of the ARZ model, offering a robust alternative to reinforcement learning by guaranteeing stability and reducing computational latency. The findings suggest that neural operators can significantly enhance the practical applicability of PDE-based control designs for dynamic systems with uncertain parameters.

Key finding

The proposed DeepONet-based adaptive control framework significantly accelerates the computation of backstepping gain kernels for traffic PDEs while theoretically guaranteeing system stability.

Methodology

simulation_modeling

Provenance

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Summary generated by qwen3.6-27b-prismaquant on 2026-06-10; verification: verified.

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