Well-posedness of networked scalar semilinear balance laws subject to nonlinear boundary control operators

Shu Xia Tang, Alexander Keimer, Alexandre M. Bayen

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Networked scalar semilinear balance laws are used as simplified macroscopic vehicular traffic models. The related initial boundary value problem is investigated, on a finite interval. The upstream boundary datum is determined by a nonlinear feedback control operator, representing the fact that traffic routing might be influenced in real time by the traffic information on the entire network. The main contribution of the present work lies in the appropriate design of nonlinear boundary control operators which meanwhile guarantee the well-posedness of the resultant systems. In detail, two different types of specific nonlinear boundary control operators are instantiated, one being Lipschitz continuous and taking into account traffic information from initial time up to present time, one using only delayed traffic information. This contribution thus presents simplified road traffic network dynamics where routing at intersections is dependent of the status of the entire network, incorporating also different classes of traffic flow.

Original languageEnglish
Title of host publication2019 IEEE 58th Conference on Decision and Control, CDC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4011-4016
Number of pages6
ISBN (Electronic)9781728113982
DOIs
StatePublished - Dec 2019
Event58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France
Duration: Dec 11 2019Dec 13 2019

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2019-December
ISSN (Print)0743-1546

Conference

Conference58th IEEE Conference on Decision and Control, CDC 2019
Country/TerritoryFrance
CityNice
Period12/11/1912/13/19

Keywords

  • Semilinear balance law
  • boundary control
  • delay
  • routing
  • traffic flow

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