Self-delayed feedback car-following control with the velocity uncertainty of preceding vehicles on gradient roads

Uphill and downhill roads are prevalent in mountainous areas freeways. Despite the advancements of vehicle-to-vehicle (V2V) communication technology, driving field vision could be still largely limited under such a complex road environment, which hinders sensors from accurately perceiving speed front vehicles. As such, fundamental question for autonomous traffic management is how to control flow associated with velocity uncertainty preceding vehicles? This paper aims answer this by devising cooperative method stabilize environment. To end, first develops model accounting vehicle’s on gradient further devises new self-delayed feedback controller based headway differences between current time step historical step. The sufficient condition where jams do not occur derived perspective frequency domain via Hurwitz criteria $$H_{\infty }$$ norm transfer functions. Bode diagram reveals that robustness closed-loop can significantly enhanced. Simulation results show key parameters (control gain coefficient delay time) designed contribute stability flow, consistent theoretical analysis conclusion.