Physics-inspired Neural Networks for Parameter Learning of Adaptive Cruise Control Systems

TL;DR

This paper tackles learning the unknown design parameters of commercially implemented ACC systems by grounding neural networks in the physics of the constant time-headway policy (CTHP). It introduces physics-inspired neural networks (PiNNs) that couple a data-driven surrogate with a physics-based residual of the CTHP longitudinal dynamics, enabling inverse optimization to recover parameters $\boldsymbol{\Omega}=[\alpha,\beta,\tau]$ from space-gap and relative-velocity data. Through synthetic and empirical car-following datasets across multiple campaigns, the approach demonstrates accurate parameter recovery and full trajectory reconstruction, while revealing that stock ACC platoons frequently exhibit ${\\cal L}_2$ and ${\\cal L}_\\infty$ string instability. Bode analysis further shows low-frequency disturbances can be amplified, underscoring the need for improved stability in practical deployments. Overall, PiNNs provide a viable offline tool for identifying ACC parameters and assessing platoon stability with potential impact on traffic flow and safety.

Abstract

This paper proposes and develops a physics-inspired neural network (PiNN) for learning the parameters of commercially implemented adaptive cruise control (ACC) systems in automotive industry. To emulate the core functionality of stock ACC systems, which have proprietary control logic and undisclosed parameters, the constant time-headway policy (CTHP) is adopted. Leveraging the multi-layer artificial neural networks as universal approximators, the developed PiNN serves as a surrogate model for the longitudinal dynamics of ACC-engaged vehicles, efficiently learning the unknown parameters of the CTHP. The PiNNs allow the integration of physical laws directly into the learning process. The ability of the PiNN to infer the unknown ACC parameters is meticulously assessed using both synthetic and high-fidelity empirical data of space-gap and relative velocity involving ACC-engaged vehicles in platoon formation. The results have demonstrated the superior predictive ability of the proposed PiNN in learning the unknown design parameters of stock ACC systems from different car manufacturers. The set of ACC model parameters obtained from the PiNN revealed that the stock ACC systems of the considered vehicles in three experimental campaigns are neither $\mathcal{L}_2$ nor $\mathcal{L}_\infty$ string stable.

Figures (8)

• Figure 1: Architecture of the proposed physics-inspired and data-informed neural network for CTHP parameter learning. The neural network on the left represents the physics-uninformed surrogate predictor $\hat{{\bm{\Xi}}}(t;\bm{\theta})= \{\hat{{\bm{\xi}}}_i(t;\bm{\theta})\}_{i=1, \ldots, M}$, while the right network depicts the physics-inspired residual and boundary conditions of the CTHP, and the data-informed cost function that penalizes deviation of the surrogate model predictions from the empirical data.
• Figure 2: Space-gap and velocity trajectories for the synthetic dataset.
• Figure 3: CTHP parameter learning and convergence.
• Figure 4: Space-gap and velocity trajectories for Ispra-Casale (Exp. #1).
• Figure 5: Velocity profiles.

Theorems & Definitions (1)

• Definition 1: Strict String Stability