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

Arash Farnam 1 Alain Sarlette 2
2 QUANTIC - QUANTum Information Circuits
MINES ParisTech - École nationale supérieure des mines de Paris, ENS Paris - École normale supérieure - Paris, SU - Sorbonne Université, Inria de Paris
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 ∞−norm sense. Moreover, we identify the disturbance acting on the leader as the main issue for string stability.
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Submitted on : Wednesday, December 4, 2019 - 9:48:17 PM
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Arash Farnam, Alain Sarlette. About strong string stability of a vehicle chain with time-headway control. CDC 2018 - IEEE Conference on Decision and Control 2018, Dec 2019, Miami, United States. ⟨hal-02394701⟩

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