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Control Problems for Conservation Laws with Traffic Applications : Modeling, Analysis, and Numerical Methods / Alexandre Bayen, Maria Laura Delle Monache, Mauro Garavello, Paola Goatin, Benedetto Piccoli.

9783030930158 (electronic bk.)
3030930157 (electronic bk.)
9783030930141 (print)

Cham, Switzerland : Birkhäuser, 2022.

English

1 online resource (xvii, 227 pages) : illustrations (some color).

10.1007/978-3-030-93015-8 doi

QA377

515/.35

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.

Includes bibliographical references and index.

Open access.

Online resource; title from PDF title page (SpringerLink, viewed April 26, 2022).

Progress in nonlinear differential equations and their applications. PNLDE subseries in control ; v. 99.

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