Reconstruction of boundary conditions from internal conditions using viability theory

Aude Hofleitner, Christian G. Claudel, Alexandre M. Bayen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

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.
Original languageEnglish (US)
Title of host publication2012 American Control Conference (ACC)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
ISBN (Print)9781457710957
DOIs
StatePublished - Jun 2012

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