Probabilistic formulation of estimation problems for a class of Hamilton-Jacobi equations

Handle URI:
http://hdl.handle.net/10754/575810
Title:
Probabilistic formulation of estimation problems for a class of Hamilton-Jacobi equations
Authors:
Hofleitner, Aude; Claudel, Christian G. ( 0000-0003-0702-6548 ) ; Bayen, Alexandre M.
Abstract:
This article presents a method for deriving the probability distribution of the solution to a Hamilton-Jacobi partial differential equation for which the value conditions are random. The derivations lead to analytical or semi-analytical expressions of the probability distribution function at any point in the domain in which the solution is defined. The characterization of the distribution of the solution at any point is a first step towards the estimation of the parameters defining the random value conditions. This work has important applications for estimation in flow networks in which value conditions are noisy. In particular, we illustrate our derivations on a road segment with random capacity reductions. © 2012 IEEE.
KAUST Department:
Electrical Engineering Program; Mechanical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Distributed Sensing Systems Laboratory (DSS)
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
Conference/Event name:
51st IEEE Conference on Decision and Control, CDC 2012
Issue Date:
Dec-2012
DOI:
10.1109/CDC.2012.6426316
Type:
Conference Paper
ISSN:
01912216
Appears in Collections:
Conference Papers; Electrical Engineering Program; Mechanical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorHofleitner, Audeen
dc.contributor.authorClaudel, Christian G.en
dc.contributor.authorBayen, Alexandre M.en
dc.date.accessioned2015-08-24T09:26:50Zen
dc.date.available2015-08-24T09:26:50Zen
dc.date.issued2012-12en
dc.identifier.issn01912216en
dc.identifier.doi10.1109/CDC.2012.6426316en
dc.identifier.urihttp://hdl.handle.net/10754/575810en
dc.description.abstractThis article presents a method for deriving the probability distribution of the solution to a Hamilton-Jacobi partial differential equation for which the value conditions are random. The derivations lead to analytical or semi-analytical expressions of the probability distribution function at any point in the domain in which the solution is defined. The characterization of the distribution of the solution at any point is a first step towards the estimation of the parameters defining the random value conditions. This work has important applications for estimation in flow networks in which value conditions are noisy. In particular, we illustrate our derivations on a road segment with random capacity reductions. © 2012 IEEE.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.titleProbabilistic formulation of estimation problems for a class of Hamilton-Jacobi equationsen
dc.typeConference Paperen
dc.contributor.departmentElectrical Engineering Programen
dc.contributor.departmentMechanical Engineering Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentDistributed Sensing Systems Laboratory (DSS)en
dc.identifier.journal2012 IEEE 51st IEEE Conference on Decision and Control (CDC)en
dc.conference.date10 December 2012 through 13 December 2012en
dc.conference.name51st IEEE Conference on Decision and Control, CDC 2012en
dc.conference.locationMaui, HIen
dc.contributor.institutionElectrical Engineering and Computer Science, UC Berkeley, CA, United Statesen
dc.contributor.institutionElectrical Engineering and Computer Sciences, Civil and Environmental Engineering, UC Berkeley, United Statesen
kaust.authorClaudel, Christian G.en
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