Exact boundary controllability for free traffic flow with Lipschitz continuous state
type: Item
instance of: scholarly article
title: Exact boundary controllability for free traffic flow with Lipschitz continuous state
zbMATH Open document ID: 1400.90098
DOI: 10.1155/2016/2743251
author: Martin Gugat
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 90B20
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 93B05
zbMATH DE Number: 6952961
Wikidata QID: Q59130733
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/2743251
OpenAlex ID: W2336734538
cites work: On kinematic waves II. A theory of traffic flow on long crowded roads
cites work: Shock Waves on the Highway
cites work: On the micro-macro limit in traffic flow
cites work: An Analysis of Traffic Flow
cites work: Q3568486
cites work: Boundary Controllability between Sub- and Supercritical Flow
cites work: Exact Boundary Controllability for 1-D Quasilinear Hyperbolic Systems with a Vanishing Characteristic Speed
cites work: Global boundary controllability of the de St. Venant equations between steady states
cites work: Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems
cites work: Adjoint-based optimization on a network of discretized scalar conservation laws with applications to coordinated ramp metering
cites work: Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models
description: scientific article; zbMATH DE number 6952961