Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Mitigating Stop-and-Go Traffic Congestion with Operator Learning

Yihuai Zhang, Ruiguo Zhong, Huan Yu

TL;DR

A novel neural operator learning framework for designing boundary control to mitigate stop-and-go congestion on freeways and proposes the physics-informed neural operator (PINO) to reduce the reliance on extensive training data.

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). 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. 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 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.

Mitigating Stop-and-Go Traffic Congestion with Operator Learning

TL;DR

A novel neural operator learning framework for designing boundary control to mitigate stop-and-go congestion on freeways and proposes the physics-informed neural operator (PINO) to reduce the reliance on extensive training data.

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). 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. 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 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.

Paper Structure

This paper contains 20 sections, 6 theorems, 73 equations, 16 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Freeway traffic control
  3. Neural operators for control of PDEs
  4. Contributions
  5. Boundary Control of the ARZ PDE Model
  6. Backstepping controller design
  7. Neural Operator Learning to Accelerate Computation of Backstepping Gain Kernels
  8. Neural operator for approximating backstepping gain kernels
  9. Physics-inform neural operator for kernel approximation
  10. Experiments
  11. Simulation and training setups
  12. PI controller
  13. PINN-based controller
  14. Simulation results of closed-loop system
  15. Simulation results of backstepping kernels
  16. ...and 5 more sections

Key Result

lemma 1

The system origin1-origin2 with boundary conditions bc_q-bc_v and initial conditions $\rho(x,0), v(x,0) \in L^2[0, L]$ under the control law control_original whose kernels are solved by ker1-ker4 is locally exponentially stable in $L_2$-sense at finite time $t_f = \frac{L}{v^\star} + \frac{L}{-\rho^

Figures (16)

  • Figure 1: The diagram of the backstepping method and the proposed neural operator framework
  • Figure 2: The diagram of physics-informed neural operator structure for backstepping kernels
  • Figure 3: Traffic density and speed evolution of the open-loop system
  • Figure 4: Closed-loop traffic density evolution with different control designs
  • Figure 5: Closed-loop traffic speed evolution with different control designs
  • ...and 11 more figures

Theorems & Definitions (14)

  • lemma 1: yu_traffic_2019
  • lemma 2: DeepONet universal approximation theorem bhan2023neuralchen1995universaldeng2022approximation
  • definition 1
  • lemma 3
  • proof
  • remark 1
  • remark 2
  • Theorem 1
  • proof
  • lemma 4
  • ...and 4 more