由于守恒定律和平衡定律在现实世界中的广泛应用，尤其是在交通流中，网络守恒定律一直是人们研究的热点。这本开放获取专著是第一本研究车辆交通建模中出现的守恒定律的不同类型控制问题的专著。讨论了四种类型的控制问题——边界控制、分散控制、分布式控制和拉格朗日控制——分别对应于入口点和通行费、路口交通信号、可变限速以及自治和通信的使用。由于守恒定律与Hamilton-Jacobi方程严格相关，因此也考虑了后者的控制。附录回顾了平衡定律初边值问题的一般理论，以及附录说明了网络守恒定律理论中的主要概念。
Control Problems for Conservation Laws with Traffic Applications: Modeling, Analysis, and Numerical Methods
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.
OR
