Exact Boundary Controllability for Free Traffic Flow with Lipschitz Continuous State

Journal article
(Original article)


Publication Details

Author(s): Gugat M
Journal: Mathematical Problems in Engineering
Publisher: Hindawi Publishing Corporation
Publication year: 2016
Volume: 2016
Pages range: 11
ISSN: 1024-123X
eISSN: 1563-5147
Language: English


Abstract


We consider traffic flow governed by the LWR model. We show that a Lipschitz continuous initial density with free-flow and sufficiently small Lipschitz constant can be controlled exactly to an arbitrary constant free-flow density in finite time by a piecewise linear boundary control function that controls the density at the inflow boundary if the outflow boundary is absorbing. Moreover, this can be done in such a way that the generated state is Lipschitz continuous. Since the target states need not be close to the initial state, our result is a global exact controllability result. The Lipschitz constant of the generated state can be made arbitrarily small if the Lipschitz constant of the initial density is sufficiently small and the control time is sufficiently long. This is motivated by the idea that finite or even small Lipschitz constants are desirable in traffic flow since they might help to decrease the speed variation and lead to safer traffic.



FAU Authors / FAU Editors

Gugat, Martin apl. Prof. Dr.
Lehrstuhl für Angewandte Mathematik


How to cite

APA:
Gugat, M. (2016). Exact Boundary Controllability for Free Traffic Flow with Lipschitz Continuous State. Mathematical Problems in Engineering, 2016, 11. https://dx.doi.org/10.1155/2016/2743251

MLA:
Gugat, Martin. "Exact Boundary Controllability for Free Traffic Flow with Lipschitz Continuous State." Mathematical Problems in Engineering 2016 (2016): 11.

BibTeX: 

Last updated on 2018-11-08 at 02:54