@article{lyu2025neural,title={Neural Operators for Adaptive Control of Traffic Flow Models},author={Lyu, Kaijing and Wang, Junmin and Zhang, Yihuai and Yu, Huan},journal={arXiv preprint arXiv:2505.07353},year={2025}}
Preprint
Adaptive Event-triggered Formation Control of Autonomous Vehicles
Ziming Wang, Yihuai Zhang, Chenguang Zhao, and Huan Yu
@article{wang2025adaptive,title={Adaptive Event-triggered Formation Control of Autonomous Vehicles},author={Wang, Ziming and Zhang, Yihuai and Zhao, Chenguang and Yu, Huan},journal={arXiv preprint arXiv:2506.06746},year={2025}}
IFAC CPDE 2025
Neural-Operator Control for Traffic Flow Models with Stochastic Demand
Yihuai Zhang, Jean Auriol, and Huan Yu
In 5th IFAC Workshop on Control of Systems Governed by Partial Differential Equations (CPDE 2025), 2025
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.
@inproceedings{zhang2025neural,title={Neural-Operator Control for Traffic Flow Models with Stochastic Demand},author={Zhang, Yihuai and Auriol, Jean and Yu, Huan},booktitle={5th IFAC Workshop on Control of Systems Governed by Partial Differential Equations (CPDE 2025)},year={2025}}
TR-C
Mitigating stop-and-go traffic congestion with operator learning
Yihuai Zhang, Ruiguo Zhong, and Huan Yu
Transportation Research Part C: Emerging Technologies, Jan 2025
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.
@article{zhang2025mitigating,title={Mitigating stop-and-go traffic congestion with operator learning},author={Zhang, Yihuai and Zhong, Ruiguo and Yu, Huan},journal={Transportation Research Part C: Emerging Technologies},volume={170},pages={104928},month=jan,year={2025},doi={10.1016/j.trc.2024.104928},publisher={Elsevier}}
2024
Automatica
Mean-square exponential stabilization of mixed-autonomy traffic PDE system
Yihuai Zhang, Huan Yu, Jean Auriol, and Mike Pereira
Control of mixed-autonomy traffic where Human-driven Vehicles (HVs) and Autonomous Vehicles (AVs) coexist on the road has gained increasing attention over the recent decades. This paper addresses the boundary stabilization problem for mixed traffic on freeways. The traffic dynamics are described by uncertain coupled hyperbolic partial differential equations (PDEs) with Markov jumping parameters, which aim to address the distinctive driving strategies between AVs and HVs. Considering that the spacing policies of AVs vary in mixed traffic, the stochastic impact area of AVs is governed by a continuous Markov chain. The interactions between HVs and AVs such as overtaking or lane changing are mainly induced by impact areas. Using backstepping design, we develop a full-state feedback boundary control law to stabilize the deterministic system (nominal system). Applying Lyapunov analysis, we demonstrate that the nominal backstepping control law is able to stabilize the traffic system with Markov jumping parameters, provided the nominal parameters are sufficiently close to the stochastic ones on average. The mean-square exponential stability conditions are derived, and the results are validated by numerical simulations.
@article{zhang2024mean,title={Mean-square exponential stabilization of mixed-autonomy traffic PDE system},author={Zhang, Yihuai and Yu, Huan and Auriol, Jean and Pereira, Mike},journal={Automatica},volume={170},pages={111859},month=dec,year={2024},doi={10.1016/j.automatica.2024.111859},publisher={Pergamon}}
Preprint
Operator Learning for Robust Stabilization of Linear Markov-Jumping Hyperbolic PDEs
@article{zhang2024operator,title={Operator Learning for Robust Stabilization of Linear Markov-Jumping Hyperbolic PDEs},author={Zhang, Yihuai and Auriol, Jean and Yu, Huan},journal={arXiv preprint arXiv:2412.09019},month=dec,year={2024}}
Preprint
Neural Operators for Adaptive Control of Freeway Traffic
Kaijing Lv, Junmin Wang, Yihuai Zhang, and Huan Yu
@article{lv2024neural,title={Neural Operators for Adaptive Control of Freeway Traffic},author={Lv, Kaijing and Wang, Junmin and Zhang, Yihuai and Yu, Huan},journal={arXiv preprint arXiv:2410.20708},month=oct,year={2024}}
L4DC
Neural operators for boundary stabilization of stop-and-go traffic
Yihuai Zhang, Ruiguo Zhong, and Huan Yu
In 6th Annual Learning for Dynamics & Control Conference, Jul 2024
@inproceedings{zhang2024neural,title={Neural operators for boundary stabilization of stop-and-go traffic},author={Zhang, Yihuai and Zhong, Ruiguo and Yu, Huan},booktitle={6th Annual Learning for Dynamics \& Control Conference},pages={554--565},month=jul,year={2024},organization={PMLR}}
ACC
Robust boundary stabilization of stochastic hyperbolic PDEs
Yihuai Zhang, Jean Auriol, and Huan Yu
In 2024 American Control Conference (ACC), Jul 2024
@inproceedings{zhang2024robust,title={Robust boundary stabilization of stochastic hyperbolic PDEs},author={Zhang, Yihuai and Auriol, Jean and Yu, Huan},booktitle={2024 American Control Conference (ACC)},pages={5333--5338},month=jul,year={2024},organization={IEEE}}
CDC
Event-Triggered Boundary Control of Mixed-Autonomy Traffic
Yihuai Zhang, and Huan Yu
In 2024 IEEE 63rd Conference on Decision and Control (CDC), Dec 2024
@inproceedings{10886427,author={Zhang, Yihuai and Yu, Huan},booktitle={2024 IEEE 63rd Conference on Decision and Control (CDC)},title={Event-Triggered Boundary Control of Mixed-Autonomy Traffic},year={2024},volume={},number={},month=dec,pages={6428-6433},organization={IEEE}}
2021
J. Dyn. Sys., Meas., Control.
Low-speed vehicle path-tracking algorithm based on model predictive control using QPKWIK solver
Yihuai Zhang, Baijun Shi, Xizhi Hu, and Wandong Ai
Journal of Dynamic Systems, Measurement, and Control, Sep 2021
@article{zhang2021low,title={Low-speed vehicle path-tracking algorithm based on model predictive control using QPKWIK solver},author={Zhang, Yihuai and Shi, Baijun and Hu, Xizhi and Ai, Wandong},journal={Journal of Dynamic Systems, Measurement, and Control},volume={143},number={12},pages={121003},month=sep,year={2021},publisher={American Society of Mechanical Engineers}}
