Stability analysis of nonlinear inviscid microscopic and macroscopic traffic flow models of bidirectional cruise-controlled vehiclesStability analysis of nonlinear inviscid microscopic and macroscopic traffic flow models of bidirectional cruise-controlled vehicles Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2022-07-132022enThe 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.The research leading to these results has received funding from the European Research Council under the European Union’s Horizon 2020 Research and Innovation programme/ ERC Grant Agreement n. [833915], project TrafficFluid.http://creativecommons.org/licenses/by-nc-nd/4.0/IMA Journal of Mathematical Control and Information392609-642Karafyllis_et_al_IMA J. Math. Control Info._39(2)_2022_preprint.pdfChania [Greece]Library of TUC2022-07-08application/pdf500.5 kBfree Karafyllis Iason Καραφυλλης Ιασων Theodosis Dionysios Θεοδοσης-Παλημερης Διονυσιος Papageorgiou Markos Παπαγεωργιου Μαρκος Oxford University Press Bidirectional adaptive cruise control Autonomous vehicles Lyapunov functions