Safety-critical Traffic Control for Mixed Autonomy Systems with Input Delay and Disturbances

While the connected automated vehicle (CAV) has been applied in vehicle-based traffic control that aims to stabilize a string of car-following human-driven vehicles (HV), the safety impact of a CAV controller on the overall traffic flow system is still an open question. In this paper, we propose a Robust Safety-critical Traffic Control (RSTC) design to impart safety for the mixed autonomy traffic system, in which the speed disturbance from a leading HV and input delay of the stabilizing CAV controller are considered. We employ Control Barrier Function (CBF) to impose safety constraints on a nominal CAV control input that achieves string stability. The key challenge lies in incorporating effect of the input delay and external disturbances into the CBF constraints. The predicted speed and spacing gap in the robust CBF design is obtained using a delay-compensating state predictor. The forward invariance of the safe set is proved given the derivative of speed disturbance, i.e., acceleration of the leading vehicle, is bounded. The safety improvement of RSTC over the nominal controller is then validated via numerical simulations.