Mean square stability conditions for platoons with lossy inter-vehicle communication channels

TL;DR

This paper establishes necessary and sufficient conditions for the mean-square stability of heterogeneous vehicle platoons with lossy communication channels, considering compensation strategies and probabilistic data loss.

Contribution

It derives new stability conditions for platoons with correlated Bernoulli communication losses, incorporating compensation strategies and linking mean-square stability to string stability.

Findings

Stability depends on controller design, compensation, and transmission success probabilities.

Conditions are both necessary and sufficient for mean-square stability.

Numerical simulations validate the theoretical conditions and illustrate different platoon behaviors.

Abstract

This paper studies the mean-square stability of heterogeneous LTI vehicular platoons with inter-vehicle communication channels affected by random data loss. We consider a discrete-time platoon system with predecessor following topology and constant time-headway spacing policy. Lossy channels are modeled by Bernoulli processes allowed to be correlated in space. We make use of a class of compensation strategies to reduce the effect of data loss. Necessary and sufficient conditions are derived to guarantee the convergence of the mean and variance of the tracking errors, which depend not only on the controller design but also on the compensation strategy and the probabilities of successful transmission. Through numerical simulations, we illustrate the theoretical results, describing different platoon behaviors. We also provide insights on the mean-square stability as a necessary condition for string stability in this stochastic setting.