@inproceedings{19dc8c295f0d41c298973707d0879f5d,

title = "Solutions to switched hamilton-jacobi equations and conservation laws using hybridcomponents",

abstract = "We investigate a class of hybrid systems driven by partial differential equations for whichthe infinite dimensional state can switch in time and in space at the same time. We consider aparticular class of such problems (switched Hamilton-Jacobi equations) and define hybridcomponents as building blocks of hybrid solutions to such problems, using viability theory. Wederive sufficient conditions for well-posedness of such problems, and use a generalized Lax-Hopfformula to compute these solutions. We illustrate the results with three examples: thecomputation of the hybrid components of a Lighthill-Whitham- Richards equation; a velocity controlpolicy for a highway system; a data assimilation problem using Lagrangian measurements generatedfrom NGSIM traffic data.",

author = "Claudel, {Christian G.} and Bayen, {Alexandre M.}",

year = "2008",

doi = "10.1007/978-3-540-78929-1_8",

language = "English (US)",

isbn = "3540789286",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "101--115",

booktitle = "Hybrid Systems",

address = "Germany",

note = "11th International Workshop on Hybrid Systems: Computation and Control, HSCC 2008 ; Conference date: 22-04-2008 Through 24-04-2008",

}