Neural-Operator Control for Traffic Flow Models with Stochastic Demand

Yihuai Zhang; Jean Auriol; Huan Yu

doi:10.1016/j.ifacol.2025.08.057

Neural-Operator Control for Traffic Flow Models with Stochastic Demand

Yihuai Zhang
, Jean Auriol
, Huan Yu

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

1 Citation (Scopus)

Abstract

In this paper, we investigated the robust stabilization problem for Aw-Rascle-Zhang (ARZ) traffic systems considering stochastic traffic demand from the upstream boundary represented by a Markov-jumping process. We propose a control law that combines operator learning with the backstepping control method. To enhance computational efficiency, the backstepping kernels used in the control law are approximated by neural operators (NOs). We demonstrate that mean-square exponential stability of the closed-loop system, with a nominal neural operator-approximated backstepping control law, can be achieved through Lyapunov analysis. The theoretical results are validated by numerical simulations. © 2025 The Authors

Original language	English
Title of host publication	5th IFAC Workshop on Control of Systems Governed by Partial Differential Equations
Subtitle of host publication	CPDE 2025
Editors	Huan Yu
Publisher	Elsevier
Number of pages	6
DOIs	https://doi.org/10.1016/j.ifacol.2025.08.057
Publication status	Published - 2025
Externally published	Yes
Event	5th Joint IFAC Workshop on Control of Systems Governed by Partial Differential, Equations, CPDE 2025 and Control of Distributed Parameter Systems, CDPS 2025 - Beijing, China Duration: 18 Jun 2025 → 20 Jun 2025 https://cpde2025.bjut.edu.cn/index.html#/home

Publication series

Name	IFAC-PapersOnLine
Publisher	Elsevier
Number	8
Volume	59
ISSN (Print)	2405-8971
ISSN (Electronic)	2405-8963

Conference

Conference	5th Joint IFAC Workshop on Control of Systems Governed by Partial Differential, Equations, CPDE 2025 and Control of Distributed Parameter Systems, CDPS 2025
Place	China
City	Beijing
Period	18/06/25 → 20/06/25
Internet address	https://cpde2025.bjut.edu.cn/index.html#/home

Research Keywords

Backstepping
Neural operators
Partial Differential Equations
Traffic control

Publisher's Copyright Statement

This full text is made available under CC-BY-NC-ND 4.0. https://creativecommons.org/licenses/by-nc-nd/4.0/

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10.1016/j.ifacol.2025.08.057

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@inproceedings{d6685a7890b54b83a40ca3c0004db4a0,

title = "Neural-Operator Control for Traffic Flow Models with Stochastic Demand",

abstract = "In this paper, we investigated the robust stabilization problem for Aw-Rascle-Zhang (ARZ) traffic systems considering stochastic traffic demand from the upstream boundary represented by a Markov-jumping process. We propose a control law that combines operator learning with the backstepping control method. To enhance computational efficiency, the backstepping kernels used in the control law are approximated by neural operators (NOs). We demonstrate that mean-square exponential stability of the closed-loop system, with a nominal neural operator-approximated backstepping control law, can be achieved through Lyapunov analysis. The theoretical results are validated by numerical simulations. {\textcopyright} 2025 The Authors",

keywords = "Backstepping, Neural operators, Partial Differential Equations, Traffic control",

author = "Yihuai Zhang and Jean Auriol and Huan Yu",

note = "Publisher Copyright: {\textcopyright} 2025 The Authors.; 5th Joint IFAC Workshop on Control of Systems Governed by Partial Differential, Equations, CPDE 2025 and Control of Distributed Parameter Systems, CDPS 2025 ; Conference date: 18-06-2025 Through 20-06-2025",

year = "2025",

doi = "10.1016/j.ifacol.2025.08.057",

language = "English",

series = "IFAC-PapersOnLine",

publisher = "Elsevier",

number = "8",

editor = "\{Huan Yu\}",

booktitle = "5th IFAC Workshop on Control of Systems Governed by Partial Differential Equations",

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url = "https://cpde2025.bjut.edu.cn/index.html\#/home",

}

Zhang, Y, Auriol, J & Yu, H 2025, Neural-Operator Control for Traffic Flow Models with Stochastic Demand. in Huan Yu (ed.), 5th IFAC Workshop on Control of Systems Governed by Partial Differential Equations: CPDE 2025. IFAC-PapersOnLine, no. 8, vol. 59, Elsevier, 5th Joint IFAC Workshop on Control of Systems Governed by Partial Differential, Equations, CPDE 2025 and Control of Distributed Parameter Systems, CDPS 2025, Beijing, China, 18/06/25. https://doi.org/10.1016/j.ifacol.2025.08.057

Neural-Operator Control for Traffic Flow Models with Stochastic Demand. / Zhang, Yihuai; Auriol, Jean; Yu, Huan.
5th IFAC Workshop on Control of Systems Governed by Partial Differential Equations: CPDE 2025. ed. / Huan Yu. Elsevier, 2025. (IFAC-PapersOnLine; Vol. 59, No. 8).

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - Neural-Operator Control for Traffic Flow Models with Stochastic Demand

AU - Zhang, Yihuai

AU - Auriol, Jean

AU - Yu, Huan

PY - 2025

Y1 - 2025

N2 - In this paper, we investigated the robust stabilization problem for Aw-Rascle-Zhang (ARZ) traffic systems considering stochastic traffic demand from the upstream boundary represented by a Markov-jumping process. We propose a control law that combines operator learning with the backstepping control method. To enhance computational efficiency, the backstepping kernels used in the control law are approximated by neural operators (NOs). We demonstrate that mean-square exponential stability of the closed-loop system, with a nominal neural operator-approximated backstepping control law, can be achieved through Lyapunov analysis. The theoretical results are validated by numerical simulations. © 2025 The Authors

AB - In this paper, we investigated the robust stabilization problem for Aw-Rascle-Zhang (ARZ) traffic systems considering stochastic traffic demand from the upstream boundary represented by a Markov-jumping process. We propose a control law that combines operator learning with the backstepping control method. To enhance computational efficiency, the backstepping kernels used in the control law are approximated by neural operators (NOs). We demonstrate that mean-square exponential stability of the closed-loop system, with a nominal neural operator-approximated backstepping control law, can be achieved through Lyapunov analysis. The theoretical results are validated by numerical simulations. © 2025 The Authors

KW - Backstepping

KW - Neural operators

KW - Partial Differential Equations

KW - Traffic control

UR - https://www.scopus.com/pages/publications/105022706331

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-105022706331 &origin=recordpage

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DO - 10.1016/j.ifacol.2025.08.057

M3 - RGC 32 - Refereed conference paper (with host publication)

AN - SCOPUS:105022706331

T3 - IFAC-PapersOnLine

BT - 5th IFAC Workshop on Control of Systems Governed by Partial Differential Equations

A2 - Huan Yu,

PB - Elsevier

T2 - 5th Joint IFAC Workshop on Control of Systems Governed by Partial Differential, Equations, CPDE 2025 and Control of Distributed Parameter Systems, CDPS 2025

Y2 - 18 June 2025 through 20 June 2025

ER -

Neural-Operator Control for Traffic Flow Models with Stochastic Demand

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Research Keywords

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