Gugat M (2016)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2016
Publisher: Hindawi Publishing Corporation
Book Volume: 2016
Pages Range: 11
Article Number: 2743251
URI: http://www.hindawi.com/journals/mpe/2016/2743251/
DOI: 10.1155/2016/2743251
Open Access Link: http://dx.doi.org/10.1155/2016/2743251
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.
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.
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