Distributed Platoon Control Under Quantization: Stability Analysis and Privacy Preservation

TL;DR

This work investigates privacy-preserving distributed platoon control under two quantization paradigms. It develops a homogeneous linear platoon model with V2V communication and derives stability guarantees: deterministic quantization yields a uniformly ultimately bounded tracking error, whereas probabilistic quantization achieves asymptotic convergence in expectation with bounded variance and provides $(0,\zeta/\\Delta)$-differential privacy. A Pareto-front framework over the quantization step $\\Delta$ characterizes the trade-off between control performance and privacy, complemented by numerical simulations across multiple topologies that validate the theoretical results. The findings indicate that probabilistic quantization offers stronger privacy protection against adversaries with auxiliary information while maintaining superior control performance compared to deterministic quantization. Overall, the paper presents a lightweight, real-time privacy mechanism for distributed CAV platoons that complements stability objectives in networked control.

Abstract

Distributed control of connected and automated vehicles has attracted considerable interest for its potential to improve traffic efficiency and safety. However, such control schemes require sharing privacy-sensitive vehicle data, which introduces risks of information leakage and potential malicious activities. This paper investigates the stability and privacy-preserving properties of distributed platoon control under two types of quantizers: deterministic and probabilistic. For deterministic quantization, we show that the resulting control strategy ensures the system errors remain uniformly ultimately bounded. Moreover, in the absence of auxiliary information, an eavesdropper cannot uniquely infer sensitive vehicle states. In contrast, the use of probabilistic quantization enables asymptotic convergence of the vehicle platoon in expectation with bounded variance. Importantly, probabilistic quantizers can satisfy differential privacy guarantees, thereby preserving privacy even when the eavesdropper possesses arbitrary auxiliary information. We further analyze the trade-off between control performance and privacy by formulating an optimization problem that characterizes the impact of the quantization step on both metrics. Numerical simulations are provided to illustrate the performance differences between the two quantization strategies.

Figures (6)

• Figure 1: Schematic of platoon system and communication topology. (a) Platoon structure with $N+1$ vehicles. Typical communication topologies: (b) BD, (c) BDL, (d) PF, (e) PLF, (f) TPF, and (g) TPLF.
• Figure 2: Performance of the distributed platoon controller \ref{['equ:DC_deterministic']} with deterministic quantization ($\Delta=1$): (a) BD, (b) BDL, (c) PF, (d) PLF, (e) TPF, and (f) TPLF.
• Figure 3: Performance of the distributed platoon controller \ref{['equ:DC_probabilistic']} with probabilistic quantization ($\Delta=1$): (a) BD, (b) BDL, (c) PF, (d) PLF, (e) TPF, and (f) TPLF.
• Figure 4: Tracking errors of distributed platoon controllers with BDL topology for $\Delta = 0.25, 0.5, 0.75, 1$: (a) Controller \ref{['equ:DC_deterministic']} with deterministic quantization; (b) Controller \ref{['equ:DC_probabilistic']} with probabilistic quantization.
• Figure 5: Privacy protection performance of two quantization approaches with the eavesdropper using the estimation scheme in \ref{['equ:estimator']}, under the BD topology: (a) Deterministic quantizer applied to platoon control; (b) Probabilistic quantizer applied to platoon control.

Theorems & Definitions (13)

• Theorem 1
• Definition 1: $\infty$-Diversity
• Remark 1
• Theorem 2
• Remark 2
• Lemma 1: Xiao2005TIT
• Lemma 2
• Theorem 3
• Definition 2: $\zeta$-Adjacency
• Definition 3: $(\epsilon, \delta)$-Differential Privacy