Control Problems for Conservation Laws with Traffic Applications

Modeling, Analysis, and Numerical Methods

Benedetto Piccoli author Alexandre Bayen author Maria Laura Delle Monache author Mauro Garavello author Paola Goatin author

Format:Hardback

Publisher:Springer Nature Switzerland AG

Published:24th Apr '22

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Control Problems for Conservation Laws with Traffic Applications cover

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.  


“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)

ISBN: 9783030930141

Dimensions: unknown

Weight: unknown

227 pages

1st ed. 2022