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