Neural Operators for Adaptive Control of Traffic Flow Models

TL;DR

This paper introduces a neural operator-based adaptive boundary control method for traffic flow models, significantly speeding up kernel computations in PDE-based control systems while maintaining stability and accuracy.

Contribution

It presents a novel use of DeepONet to efficiently approximate kernel functions in PDE-based adaptive control, reducing computational costs substantially.

Findings

DeepONet accelerates kernel computation by nearly 100 times.

The method maintains system stability with low approximation loss.

Simulations confirm effective adaptive control of traffic flow.

Abstract

The uncertainty in human driving behaviors leads to stop-and-go instabilities in freeway traffic. The traffic dynamics are typically modeled by the Aw-Rascle-Zhang (ARZ) Partial Differential Equation (PDE) models, in which the relaxation time parameter is usually unknown or hard to calibrate. This paper proposes an adaptive boundary control design based on neural operators (NO) for the ARZ PDE systems. In adaptive control, solving the backstepping kernel PDEs online requires significant computational resources at each timestep to update estimates of the unknown system parameters. To address this, we employ DeepONet to efficiently map model parameters to kernel functions. Simulations show that DeepONet generates kernel solutions nearly two orders of magnitude faster than traditional solvers while maintaining a loss on the order of \(10^{-2}\). Lyapunov analysis further validates the stability of the system when using DeepONet-approximated kernels in the adaptive controller. This result suggests that neural operators can significantly accelerate the acquisition of adaptive controllers for traffic control.