Solutions to switched hamilton-jacobi equations and conservation laws using hybridcomponents

Christian Claudel, Alexandre M. Bayen

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

11 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationHybrid Systems
Subtitle of host publicationComputation and Control - 11th International Workshop, HSCC 2008, Proceedings
Pages101-115
Number of pages15
DOIs
StatePublished - Dec 1 2008
Event11th International Workshop on Hybrid Systems: Computation and Control, HSCC 2008 - St. Louis, MO, United States
Duration: Apr 22 2008Apr 24 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4981 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other11th International Workshop on Hybrid Systems: Computation and Control, HSCC 2008
CountryUnited States
CitySt. Louis, MO
Period04/22/0804/24/08

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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