Sliding mode control based stabilization of cascaded traffic flow with boundary disturbance

This paper studies the congestion control problem of traffic dynamics on two cascaded freeway segments with different road conditions, where there exists an on-ramp at the junction of the two traffic flow segments, along with the flow rate fluctuation. The cascaded traffic flow is described by a coupled hyperbolic system based on the Aw–Rascle–Zhang traffic flow model, consisting of two subsystems of second-order nonlinear partial differential equations that describe the evolution of traffic density and velocity on each segment. To stabilize the two cascaded traffic flow segments to their steady states simultaneously, we design a boundary control law for the on-ramp metering with boundary input disturbance induced by the flow rate fluctuation at the junction, by using the backstepping method combined with sliding mode control approach. Additionally, we prove the existence of the closed-loop system’s solution, and demonstrate that the system is driven to the designed sliding surface in finite time and the system exhibits exponential stability on the sliding surface. Finally, we present numerical simulations to demonstrate the controller’s effectiveness in mitigating unknown boundary input disturbance and simultaneously stabilizing the cascaded traffic flow.