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This paper develops a full-state feedback controller that damps outoscillations in traffic density and traffic velocity whose dynamical behavioris governed by the linearized two-class Aw-Rascle (AR) model. Thereby, thetraffic is considered to be in the congested regime and subdivided in twoclasses whereas each class represents vehicles with the same size and driver'sbehavior. The macroscopic second-order two-class AR model consists of fourfirst order hyperbolic partial differential equations (PDEs) and introduces aconcept of area occupancy to depict the mixed density of two-class vehicles inthe traffic. Moreover, the linearized model equations show heterodirectionalbehavior with both positive and negative characteristic speeds in the congestedregime. The control objective is to achieve convergence to a constantequilibrium in finite time. The control input is realized by ramp meteringacting at the outlet of the considered track section. The backstepping methodis employed to design full-state feedback for the $4\times 4$ hyperbolic PDEs.The performance of the full-state feedback controller is verified bysimulation.

Suppression of Oscillations in Two-Class Traffic by Full-State Feedback