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Traffic flow control on cascaded roads by event‐triggered output feedback
Author(s) -
Espitia Nicolas,
Auriol Jean,
Yu Huan,
Krstic Miroslav
Publication year - 2022
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.6122
Subject(s) - control theory (sociology) , backstepping , metering mode , traffic flow (computer networking) , dwell time , controller (irrigation) , computer science , boundary (topology) , event (particle physics) , upstream (networking) , control (management) , mathematics , engineering , adaptive control , physics , mechanical engineering , medicine , clinical psychology , agronomy , mathematical analysis , computer security , quantum mechanics , artificial intelligence , biology , computer network
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.