Platooning of Connected Vehicles with Undirected Topologies: Robustness Analysis and Distributed H-infinity Controller Synthesis

TL;DR

This paper analyzes the robustness of vehicle platoons with undirected communication topologies and develops a scalable distributed H-infinity controller synthesis method, highlighting the impact of topology and leader information on robustness.

Contribution

It introduces a unified model for homogeneous platoons, provides explicit robustness scaling trends, and proposes a scalable controller synthesis procedure considering topology optimization.

Findings

Robustness measure scales explicitly with platoon size.

Communication topology significantly affects robustness and control.

Coordination of mini-platoons is effective for large-scale systems.

Abstract

This paper considers the robustness analysis and distributed $\mathcal{H}_{\infty}$ (H-infinity) controller synthesis for a platoon of connected vehicles with undirected topologies. We first formulate a unified model to describe the collective behavior of homogeneous platoons with external disturbances using graph theory. By exploiting the spectral decomposition of a symmetric matrix, the collective dynamics of a platoon is equivalently decomposed into a set of subsystems sharing the same size with one single vehicle. Then, we provide an explicit scaling trend of robustness measure $\gamma$-gain, and introduce a scalable multi-step procedure to synthesize a distributed $\mathcal{H}_{\infty}$ controller for large-scale platoons. It is shown that communication topology, especially the leader's information, exerts great influence on both robustness performance and controller synthesis. Further, an intuitive optimization problem is formulated to optimize an undirected topology for a platoon system, and the upper and lower bounds of the objective are explicitly analyzed, which hints us that coordination of multiple mini-platoons is one reasonable architecture to control large-scale platoons. Numerical simulations are conducted to illustrate our findings.