Stability and String Stability of Car-following Models with Reaction-time Delay

Guy Fayolle (1) , Jean-Marc Lasgouttes (1) , Carlos Flores (2)

1 RITS - Robotics & Intelligent Transportation Systems
2 ITS - Institute of Transportation Studies [Berkeley]

We investigate the transfer function emanating from the linearization of a car-following model, when taking into account a driver reaction time. This leads to nontrivial stability conditions, which are explicitly given. They are in particular satisfied whenever string stability holds. We also show how this reaction time can introduce a partial string stability, where the transfer function modulus remains smaller or equal to 1 up to some critical frequency. We explore conditions in the parameter space discriminating between the different regimes. This is a preliminary step of a forthcoming work about traffic stabilization via connected automated vehicles.

Mots clés: Trafic control; Modeling; Stability of linear systems; Methods of the complexvariable.; Transportation networks

Domaines: Mathématiques [math]; Variables complexes [math.CV]; Automatique / Robotique

Guy Fayolle, Jean-Marc Lasgouttes, Carlos Flores. Stability and String Stability of Car-following Models with Reaction-time Delay. 2020. ⟨hal-03697661v7⟩