About strong string stability of a vehicle chain with time-headway control

TL;DR

This paper investigates the limits of string stability in vehicle chains with time-headway control, showing that certain stability criteria cannot be achieved with linear controllers, but a PD controller can ensure stability in the infinity-norm sense.

Contribution

It proves the impossibility of achieving certain string stability criteria with linear controllers and identifies the leader disturbance as a key factor, proposing a PD controller for practical stability.

Findings

Linear controllers cannot bound the influence from input to output independently of chain length in 2-norm.

A PD controller can guarantee string stability in the infinity-norm sense.

Leader disturbance is identified as the main challenge for string stability.

Abstract

This paper deals with the problem of string stability in a chain of acceleration-controlled vehicles, i.e. how input disturbances affect the distributed system for very long chains. There exist variants of string stability, like avoiding that a local disturbance gets amplified along the chain, or more strongly ensuring that the output vector's p-norm remains bounded for any bounded vector of input disturbances independently of the string length. They are all impossible to achieve with any linear controller if the vehicles only use relative information of few vehicles in front. Previous work has shown that adding absolute velocity into the controller, allows to at least avoid amplification of a local disturbance. In this paper, we consider the stronger definitions of string stability, under this same relaxation of using absolute velocity in the controller. We prove that the influence from input vector to output vector cannot be bounded independently of chain length in the most popular 2-norm sense, with any bounded stabilizing linear controller; while a proportional derivative (PD) controller can guarantee it in the practically relevant infinity-norm sense. Moreover, we identify the disturbance acting on the leader as the main issue for string stability.