Bayen A. Control Problems for Conservation Laws with Traffic Applications...2022

Textbook in PDF format

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.
1 Introduction
2 Boundary Control of Conservation Laws Exhibiting Shocks
3 Decentralized Control of Conservation Laws on Graphs
4 Distributed Control for Conservation Laws
5 Lagrangian Control of Conservation Laws and Mixed Models
6 Control Problems for Hamilton-Jacobi Equations
A Conservation and Balance Laws and Boundary Value Problems
B Models for Vehicular Traffic and Conservation Laws on Networks