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Stability analysis of nonlinear inviscid microscopic and macroscopic traffic flow models of bidirectional cruise-controlled vehicles

Karafyllis Iason, Theodosis Dionysios, Papageorgiou Markos

Πλήρης Εγγραφή


URI: http://purl.tuc.gr/dl/dias/2FDCAB58-B1A7-4F5C-B3D6-40FA166A7DDB
Έτος 2022
Τύπος Δημοσίευση σε Περιοδικό με Κριτές
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Βιβλιογραφική Αναφορά I. Karafyllis, D. Theodosis, and M. Papageorgiou, “Stability analysis of nonlinear inviscid microscopic and macroscopic traffic flow models of bidirectional cruise-controlled vehicles,” IMA J. Math. Control Info., vol. 39, no. 2, pp. 609–642, June 2022, doi: 10.1093/imamci/dnac003. https://doi.org/10.1093/imamci/dnac003
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Περίληψη

The paper introduces a new bidirectional microscopic inviscid Adaptive Cruise Control (ACC) model that uses only spacing information from the preceding and following vehicles in order to select the proper control action to avoid collisions and maintain a desired speed. KL estimates that guarantee uniform convergence of the ACC model to the set of equilibria are provided. Moreover, the corresponding macroscopic model is derived, consisting of a conservation equation and a momentum equation that contains a nonlinear relaxation term. It is shown that, if the density is sufficiently small, then the macroscopic model has a solution that approaches exponentially the equilibrium speed (in the sup norm) while the density converges exponentially to a traveling wave. Numerical simulations are also provided, illustrating the properties of the microscopic and macroscopic inviscid ACC models.

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