Neural-Operator Control for Traffic Flow Models with Stochastic Demand
DOI: 10.1016/j.ifacol.2025.08.057
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Summary
This paper addresses the robust stabilization of macroscopic traffic flow models subject to stochastic demand uncertainties. Specifically, it focuses on the Aw–Rascle–Zhang (ARZ) model, a second-order partial differential equation (PDE) system that captures stop-and-go traffic oscillations. The primary motivation is the limitation of traditional backstepping control methods, which, while theoretically sound for deterministic systems, are computationally expensive to implement and struggle with the uncertainties inherent in real-world traffic, such as stochastic upstream demand and varying driver behaviors. The authors propose a control strategy that combines backstepping with neural operators (NOs) to efficiently approximate control kernels and handle stochasticity modeled as a Markov-jumping process. The methodology involves linearizing the ARZ model around an equilibrium state and transforming it into Riemann coordinates. The authors employ the backstepping method to design a control law that stabilizes the system, but instead of solving the complex kernel equations analytically, they approximate the backstepping kernels using DeepONet-based neural operators. This approach allows the controller to map system parameters to control kernels efficiently. The stochastic nature of the traffic demand is represented by continuous Markov chains affecting the system parameters. The theoretical framework relies on Lyapunov analysis to prove stability. The authors define a stochastic Lyapunov functional and utilize the infinitesimal generator to analyze the system's behavior under Markov-jumping parameters. They establish bounds on the approximation errors introduced by the neural operators and the deviations caused by stochastic parameter jumps. The main finding is that the closed-loop system achieves mean-square exponential stability under the proposed neural-operator-approximated control law. The authors prove that if the approximation error of the neural operator is sufficiently small and the stochastic parameters remain close to their nominal values on average, the system states converge to equilibrium. This result is formalized in Theorem 6, which provides specific conditions on the approximation error and the expected deviation of stochastic parameters to guarantee stability. Numerical simulations on a 500-meter road section validate these theoretical results. The simulations demonstrate that the controller effectively stabilizes the traffic flow despite stochastic variations in upstream demand, confirming the robustness and computational efficiency of the NO-based approach compared to traditional methods. The significance of this work lies in bridging the gap between rigorous PDE control theory and data-driven operator learning. By demonstrating that neural operators can effectively approximate backstepping kernels for stochastic systems, the paper offers a scalable solution for real-time traffic management. This approach overcomes the computational bottlenecks of solving kernel equations online and provides theoretical guarantees for systems with uncertainty. The findings imply that operator learning can be reliably integrated into safety-critical control systems, enhancing the performance and robustness of intelligent transportation systems under unpredictable conditions.
Key finding
A neural operator-approximated backstepping control law achieves mean-square exponential stability for Aw-Rascle-Zhang traffic systems with stochastic demand modeled as a Markov-jumping process.
Methodology
simulation_modeling
Provenance
The full processing record for this entry. Every stage of this paper's journey through the pipeline is logged — what ran, with which tool and model, how many attempts it took, and when it last completed. Discovered via author_sweep_intake on 2026-05-28.
| Stage | Outcome | Tool | Model | Prompt | Attempts | Completed |
|---|---|---|---|---|---|---|
| discover | success | author_sweep | — | — | 2 | 2026-05-28 |
| archive | success | canonical_url | — | — | 5 | 2026-06-06 |
| extract | success | cached | — | — | 3 | 2026-06-10 |
| clean | success | clean | — | — | 1 | 2026-06-04 |
| chunk | success | chunk | — | — | 1 | 2026-06-04 |
| embed | success | embed | Qwen/Qwen3-Embedding-8B | — | 1 | 2026-06-04 |
| enrich | success | — | — | — | 1 | 2026-05-28 |
| promote | success | — | — | — | 1 | 2026-06-04 |
| summarize | success | llm | qwen3.6-27b-prismaquant | summ-v5 | 2 | 2026-06-10 |
| tag | success | vector_similarity | — | — | 15 | 2026-06-11 |
| verify | success | — | — | — | 2 | 2026-06-10 |
Summary generated by qwen3.6-27b-prismaquant on 2026-06-10; verification: verified.
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- Theoretical Contribution: computational model