Mistuning-based Control Design to Improve Closed-Loop Stability of Vehicular Platoons

TL;DR

This paper analyzes the stability of vehicular platoons using PDE approximation and demonstrates that small mistuning of controllers can significantly improve the asymptotic stability as the number of vehicles increases.

Contribution

It introduces a PDE-based analysis for platoon stability and shows that mistuning controllers enhances stability bounds from O(1/N^2) to O(1/N).

Findings

PDE model explains stability loss with increasing vehicles.

Uniform controllers lead to eigenvalues approaching zero as O(1/N^2).

Mistuning improves stability to O(1/N) for large platoons.

Abstract

We consider a decentralized bidirectional control of a platoon of N identical vehicles moving in a straight line. The control objective is for each vehicle to maintain a constant velocity and inter-vehicular separation using only the local information from itself and its two nearest neighbors. Each vehicle is modeled as a double integrator. To aid the analysis, we use continuous approximation to derive a partial differential equation (PDE) approximation of the discrete platoon dynamics. The PDE model is used to explain the progressive loss of closed-loop stability with increasing number of vehicles, and to devise ways to combat this loss of stability. If every vehicle uses the same controller, we show that the least stable closed-loop eigenvalue approaches zero as O(1/N^2) in the limit of a large number (N) of vehicles. We then show how to ameliorate this loss of stability by small amounts of "mistuning", i.e., changing the controller gains from their nominal values. We prove that with arbitrary small amounts of mistuning, the asymptotic behavior of the least stable closed loop eigenvalue can be improved to O(1/N) All the conclusions drawn from analysis of the PDE model are corroborated via numerical calculations of the state-space platoon model.