Control Problems for Conservation Laws with Traffic Applications

Inside this Book

If you make use of this material, you may credit the authors as follows:

Bayen Alexandre et al., "Control Problems for Conservation Laws with Traffic Applications", Springer Nature, 2022, DOI: 10.1007/978-3-030-93015-8, License: http://creativecommons.org/licenses/by/4.0/

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.

Keywords

Hyperbolic Conservation Laws, Vehicular Traffic Modeling, Control Problems Conservation Laws, Hamilton-jacobi Equations, Conservation Laws On Networks, Lighthill-whitham-richard Model, Topological Graphs

Rights | License

Except where otherwise noted, this item has been published under the following license:

Takedown policy

If you believe that this publication infringes copyright, please contact us at info@jecasa-ltd.com and provide relevant details so that we can investigate your claim.