This article deals with the observation problem in traffic flow theory. The model used is the quasiilinear viscous Burgers equation. Instead of using the traditional fixed sensors to estimate the state of the traffic at given points, the measurements here are obtained from Probe Vehicles (PVs). We propose then a moving dynamic boundary observer whose boundaries are defined by the trajectories of the PVs. The main result of this article is the exponential convergence of the observation error, and, in some cases, its finite-time convergence. Finally, numerical simulations show that it is possible to observe the traffic in the congested, free-flow, and mixed regimes provided that the number of PVs is large enough.
Bibliographical noteKAUST Repository Item: Exported on 2021-03-23
Acknowledged KAUST grant number(s): OSR-2019-CRG8-4033
Acknowledgements: The research leading to these results is partially funded by the KAUST Office of Sponsored Research under Award No. OSR-2019-CRG8-4033, the Swedish Foundation for Strategic Research and Knut and Alice Wallenberg Foundation. The authors are affiliated with the Wallenberg AI, Autonomous Systems and Software Program (WASP).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.