String and robust stability of connected vehicle systems with delayed feedback

Two important characteristics of a connected vehicle system are string stability (i.e., disturbance in state variables should not propagate along the platoon) and robustness to parametric uncertainties. In this paper, we study these properties for a platoon of vehicles driving on a single-lane straight road. Specifically, we model individual vehicle’s dynamics by the Classical Car-Following Model (CCFM) and the Modified Optimal Velocity Model (MOVM). These models capture the reaction delays inherent in such a setting. First, we focus on string stability. For both models, we derive a sufficient condition for string stability. We then concentrate on the robustness to uncertainties in the parameters of the said models. For both models, we derive bounds on the reaction delay to ensure (a) pairwise robust stability, and (b) platoon robust stability, when the remaining model parameters lie in an interval. Finally, we compare our results with conditions for these models to be locally asymptotically stable. This brings forth the additional constraints imposed on the reaction delay to achieve string and robust stability. Our results may provide design guidelines for futuristic connected vehicle systems. Additionally, from a technological perspective, our results suggest the sufficiency of using only on-board sensors for all forms of local stability except platoon robust stability.