Control Problems for Conservation Laws with Traffic Applications: Modeling, Analysis, and Numerical Methods

This open-access monograph investigates control problems for conservation laws in vehicular traffic modeling, discussing boundary, decentralized, distributed, and Lagrangian control, as well as Hamilton-Jacobi equations. It also includes an appendix reviewing the general theory of initial-boundary value problems and illustrating the main concepts of conservation laws on networks.

Format: Hardback
Length: 227 pages
Publication date: 24 April 2022
Publisher: Springer Nature Switzerland AG

The study of conservation and balance laws on networks has garnered significant attention due to their extensive applications in real-world processes, particularly in the realm of traffic flow. In this open-access monograph, we embark on a pioneering exploration of diverse control problems associated with conservation laws in the modeling of vehicular traffic. We address four distinct types of control challenges: boundary control, decentralized control, distributed control, and Lagrangian control. These correspond to entrance points and tolls, traffic signals at junctions, variable speed limits, and the integration of autonomy and communication. Furthermore, we delve into the control of Hamilton-Jacobi equations, recognizing their intimate connection with conservation laws. To enhance the understanding of these concepts, we include an appendix reviewing the general theory of initial-boundary value problems for balance laws. Additionally, an appendix is provided to illustrate the key principles of conservation laws on networks. This comprehensive monograph aims to shed light on the intricate dynamics of conservation laws and their practical implications in the field of traffic management, paving the way for future research and innovation.

The study of conservation and balance laws on networks has garnered significant attention due to their extensive applications in real-world processes, particularly in the realm of traffic flow. In this open-access monograph, we embark on a pioneering exploration of diverse control problems associated with conservation laws in the modeling of vehicular traffic. We address four distinct types of control challenges: boundary control, decentralized control, distributed control, and Lagrangian control. These correspond to entrance points and tolls, traffic signals at junctions, variable speed limits, and the integration of autonomy and communication. Furthermore, we delve into the control of Hamilton-Jacobi equations, recognizing their intimate connection with conservation laws. To enhance the understanding of these concepts, we include an appendix reviewing the general theory of initial-boundary value problems for balance laws. Additionally, an appendix is provided to illustrate the key principles of conservation laws on networks. This comprehensive monograph aims to shed light on the intricate dynamics of conservation laws and their practical implications in the field of traffic management, paving the way for future research and innovation.

Weight: 541g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030930141
Edition number: 1st ed. 2022