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Control problems for conservation laws with traffic applications [electronic resource] : modeling, analysis, and numerical methods / by Alexandre Bayen, Maria Laura Delle Monache, Mauro Garavello, Paola Goatin, Benedetto Piccoli.

By: Contributor(s): Material type: TextTextSeries: PNLDE Subseries in Control ; 99Publisher: Cham : Springer International Publishing : Imprint: Birkhäuser, 2022Edition: 1st ed. 2022Description: XVII, 227 p. 92 illus., 47 illus. in color. online resourceContent type:
Media type:
Carrier type:
ISBN:
  • 9783030930158
Subject(s): Additional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification:
  • 515.35 23
Online resources:
Contents:
Introduction -- Boundary Control -- Decentralized Control -- Distributed Control -- Lagrangian Control -- Hamilton-Jacobi Equations -- Appendix A: Balance Laws with Boundary -- Conservation Laws on Networks.
In: Springer Nature eBookSummary: Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different types of control problems for conservation laws that arise in the modeling of vehicular traffic. Four types of control problems are discussed - boundary, decentralized, distributed, and Lagrangian control - corresponding to, respectively, entrance points and tolls, traffic signals at junctions, variable speed limits, and the use of autonomy and communication. Because conservation laws are strictly connected to Hamilton-Jacobi equations, control of the latter is also considered. An appendix reviewing the general theory of initial-boundary value problems for balance laws is included, as well as an appendix illustrating the main concepts in the theory of conservation laws on networks. .
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Introduction -- Boundary Control -- Decentralized Control -- Distributed Control -- Lagrangian Control -- Hamilton-Jacobi Equations -- Appendix A: Balance Laws with Boundary -- Conservation Laws on Networks.

Open Access

Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different types of control problems for conservation laws that arise in the modeling of vehicular traffic. Four types of control problems are discussed - boundary, decentralized, distributed, and Lagrangian control - corresponding to, respectively, entrance points and tolls, traffic signals at junctions, variable speed limits, and the use of autonomy and communication. Because conservation laws are strictly connected to Hamilton-Jacobi equations, control of the latter is also considered. An appendix reviewing the general theory of initial-boundary value problems for balance laws is included, as well as an appendix illustrating the main concepts in the theory of conservation laws on networks. .

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