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 (Autoren)

Buch | Softcover

XVII, 227 Seiten

2022 | 1st ed. 2022
Springer International Publishing (Verlag)
978-3-030-93017-2 (ISBN)

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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.

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.

Introduction.- Boundary Control.- Decentralized Control.- Distributed Control.- Lagrangian Control.- Hamilton-Jacobi Equations.- Appendix A: Balance Laws with Boundary.- 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)

Erscheinungsdatum	26.04.2022
Reihe/Serie	PNLDE Subseries in Control
Reihe/Serie	Progress in Nonlinear Differential Equations and Their Applications
Zusatzinfo	XVII, 227 p. 92 illus., 47 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	385 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Wirtschaft ► Betriebswirtschaft / Management
Schlagworte	Conservation Laws on Networks • Control Problems Conservation Laws • Hamilton-Jacobi equations • hyperbolic conservation laws • Lighthill-Whitham-Richard Model • open access • Topological Graphs • Vehicular Traffic Modeling
ISBN-10	3-030-93017-3 / 3030930173
ISBN-13	978-3-030-93017-2 / 9783030930172
Zustand	Neuware