Event-triggered Boundary Control of Mixed-autonomy Traffic

Control problems of mixed-autonomy traffic system consisting of both Human-driven Vehicles (HV) and Autonomous Vehicles (AV) have gained increasing attention. This paper is focused on suppressing traffic oscillations of the mixed-autonomy traffic system using boundary control design. The mixed traffic dynamics are described by a 4 x 4 hyperbolic partial differential equations (PDE) which governs propagation of four properties in traffic including density of HV, density of AV, friction between two classes of vehicles from driving interactions, and averaged velocity. We propose event-triggered boundary control design since control signal of traffic light on ramp or varying speed limit cannot be updated in a continuous time fashion. We apply event-triggered mechanism for a PDE backstepping controller and obtain dynamic triggering condition. Lyapunov analysis is conducted to prove the exponential stability of the closed loop system with the event-triggered controller. Numerical simulation demonstrates how car-following spacing of AV affects event-triggering mechanism of control input in mixed-autonomy traffic.