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Control Problems for Conservation Laws with Traffic Applications
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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.
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Keywords
- Business & management
- Calculus & mathematical analysis
- Conservation Laws on Networks
- Control Problems Conservation Laws
- Cybernetics & systems theory
- Economics, finance, business & management
- Hamilton-Jacobi Equations
- Hyperbolic Conservation Laws
- Information theory
- Lighthill-Whitham-Richard Model
- Mathematics
- Mathematics & science
- Operational research
- Reference, information & interdisciplinary subjects
- Research & information: general
- thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general::GPF Information theory::GPFC Cybernetics and systems theory
- thema EDItEUR::K Economics, Finance, Business and Management::KJ Business and Management::KJT Operational research
- thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis
- Topological Graphs
- Vehicular Traffic Modeling
Links
DOI: 10.1007/978-3-030-93015-8Editions