Control problems for conservation laws with traffic applications : modeling, analysis, and numerical methods / by Alexandre Bayen, Maria Laura Delle Monache, Mauro Garavello, Paola Goatin, Benedetto Piccoli
Introduction -- Boundary Control -- Decentralized Control -- Distributed Control -- Lagrangian Control -- Hamilton-Jacobi Equations -- Appendix A: Balance Laws with Boundary -- Conservation Laws on Networks
Open access
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
