Safe Stabilizing Control of Traffic Systems With Simultaneous State and Actuator Delays

The integration of connectivity and autonomy in vehicles has shown great promise in smoothing traffic by a leading connected automated vehicle (CAV), which can be achieved by designing cruising control strategies to regulate the velocity and spacing of a string of follower vehicles. Safety verification of these stabilizing traffic controllers in real-world traffic systems, where delays stem from human reaction times and sensor/actuator latency, remains an open research question. In this paper, we solve the safe stabilization of a class of traffic systems with simultaneous state and actuator delays, using the control barrier function (CBF). A predictor with bounded prediction error is designed to compensate for the actuator delay and state delays. Delay-compensating CBF constraints are designed to guarantee formal safety under simultaneous state and actuator delays. We synthesize a safety-critical controller by solving a Quadratic Programming problem that minimizes deviation from a nominal stabilizing traffic controller. Numerical simulations discuss the safety impact of simultaneous reaction delay of human drivers and the actuator delay of CAV in two safety-critical scenarios and validate the proposed CBF safety constraints.