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Birkhäuser

Control Problems for Conservation Laws with Traffic Applications

Modeling, Analysis, and Numerical Methods

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  • Open Access
  • © 2022

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Overview

  • This book is open access, which means that you have free and unlimited access
  • First monograph on different types of control problems for conservation laws arising in vehicular traffic modeling
  • Describes mathematical approaches that can be used to develop solutions to traffic problems
  • Appendices provide background on the mathematical theory of conservation and balance laws

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 99)

Part of the book sub series: PNLDE Subseries in Control (PNLDE-SC)

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Table of contents (6 chapters)

Keywords

About this book

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.  


Reviews

“This book provides comprehensive and self-contained descriptions and analysis of such problems and can be used for a one semester course at graduate or advanced undergraduate level.” (Giuseppe Maria Coclite, Mathematical Reviews, April, 2024)

Authors and Affiliations

  • Institute of Transportation Studies, University of California, Berkeley, USA

    Alexandre Bayen

  • Department of Civil and Environmental Engineering, Part of the work was done while the author was at Inria Grenoble-Rhône Alpes (France), University of California, Berkeley, USA

    Maria Laura Delle Monache

  • Department of Mathematics & Applications, University of Milano-Bicocca, Milan, Italy

    Mauro Garavello

  • Inria, Research Center of Université Côte d’Azur, Sophia Antipolis, France

    Paola Goatin

  • Department of Mathematical Sciences, Rutgers University, Camden, USA

    Benedetto Piccoli

About the authors

Alexandre Bayen is a Professor of Electrical Engineering and Computer Science at UC Berkeley, and the Director of the Institute of Transportation Studies. 

Maria Laura Delle Monache is a research scientist at Inria, the French National Institute for computer Science and Applied Mathematics. 


Mauro Garavello is an Associate Professor of Mathematical Analysis at the University of Milano Bicocca.


Paola Goatin is Research Director a Inria, the French National Institute for Research in Digital Science and Technology


Benedetto Piccoli is Distinguished Professor and the Joseph and Loretta Lopez Chair Professor of Mathematics at Rutgers University - Camden. He also serves as Vice Chancellor for Research.

Bibliographic Information

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