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    Reconstruction of boundary conditions from internal conditions using viability theory

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    Type
    Conference Paper
    Authors
    Hofleitner, Aude
    Claudel, Christian G. cc
    Bayen, Alexandre M.
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Distributed Sensing Systems Laboratory (DSS)
    Electrical Engineering Program
    Mechanical Engineering Program
    Physical Science and Engineering (PSE) Division
    Date
    2012-06
    Permanent link to this record
    http://hdl.handle.net/10754/575806
    
    Metadata
    Show full item record
    Abstract
    This article presents a method for reconstructing downstream boundary conditions to a HamiltonJacobi partial differential equation for which initial and upstream boundary conditions are prescribed as piecewise affine functions and an internal condition is prescribed as an affine function. Based on viability theory, we reconstruct the downstream boundary condition such that the solution of the Hamilton-Jacobi equation with the prescribed initial and upstream conditions and reconstructed downstream boundary condition satisfies the internal value condition. This work has important applications for estimation in flow networks with unknown capacity reductions. It is applied to urban traffic, to reconstruct signal timings and temporary capacity reductions at intersections, using Lagrangian sensing such as GPS devices onboard vehicles.
    Citation
    Hofleitner, A., Claudel, C., & Bayen, A. (2012). Reconstruction of boundary conditions from internal conditions using viability theory. 2012 American Control Conference (ACC). doi:10.1109/acc.2012.6314947
    Publisher
    Institute of Electrical and Electronics Engineers (IEEE)
    Journal
    2012 American Control Conference (ACC)
    Conference/Event name
    American Control Conference (ACC), 2012
    ISBN
    9781457710957
    DOI
    10.1109/acc.2012.6314947
    ae974a485f413a2113503eed53cd6c53
    10.1109/acc.2012.6314947
    Scopus Count
    Collections
    Conference Papers; Physical Science and Engineering (PSE) Division; Electrical and Computer Engineering Program; Mechanical Engineering Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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