Traffic flow control on cascaded roads by event‐triggered output feedback. (1st April 2022)

• Record Type: Journal Article
• Authors: Espitia, Nicolas; Auriol, Jean; Yu, Huan; Krstic, Miroslav
• Is Part Of: International journal of robust and nonlinear control. Volume 32:Number 10(2022)
• Page Start: 5919
• Page End: 5949
• Publication Date: 2022-04-01
• Subjects: backstepping control design -- event‐triggered control -- PDE‐based control -- ramp metering -- traffic flow model; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.6122
• Languages: English
• ISSNs: 1049-8923

Abstract

Abstract: In this article, we propose an event‐triggered output‐feedback controller that guarantees the simultaneous stabilization of traffic flow on two connected roads. The density and velocity traffic dynamics are described with the linearized Aw‐Rascle‐Zhang macroscopic traffic partial differential equation model, which results in a coupled hyperbolic system. The control objective is to simultaneously stabilize the upstream and downstream traffic to a given spatially uniform constant steady‐state that is in the congested regime. To suppress stop‐and‐go traffic oscillations on the cascaded roads, we consider a ramp metering strategy that regulates the traffic flow rate entering from the on‐ramp to the mainline freeway. The ramp metering is located at the outlet with only boundary measurements of flow rate and velocity. Under the event‐triggered scheme, the control signal is only updated when an event triggering condition is satisfied. Compared with the continuous input signal, the event‐triggered boundary output control presents a more realistic setting to implement by ramp metering on a digital platform. The event‐triggered control design relies on the emulation of the backstepping boundary output feedback and on a dynamic event‐triggered strategy to determine the time instants at which the control value must be updated. We prove that there is a uniform minimal dwell‐time (independent of initial conditions), thus avoiding the Zeno phenomenon. We guarantee the exponential convergence of the closed‐loop system under the proposed event‐triggered control. A numerical example illustrates the results.