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

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

doi:10.1109/CDC.2012.6426316

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

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

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.

Original language	English (US)
Title of host publication	2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	3531-3537
Number of pages	7
ISBN (Print)	9781467320665
DOIs	https://doi.org/10.1109/CDC.2012.6426316
State	Published - Dec 2012

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10.1109/CDC.2012.6426316

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title = "Probabilistic formulation of estimation problems for a class of Hamilton-Jacobi equations",

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. {\textcopyright} 2012 IEEE.",

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

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Probabilistic formulation of estimation problems for a class of Hamilton-Jacobi equations. / Hofleitner, Aude; Claudel, Christian G.; Bayen, Alexandre M.
2012 IEEE 51st IEEE Conference on Decision and Control (CDC). Institute of Electrical and Electronics Engineers (IEEE), 2012. p. 3531-3537.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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T1 - Probabilistic formulation of estimation problems for a class of Hamilton-Jacobi equations

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AU - Claudel, Christian G.

AU - Bayen, Alexandre M.

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N2 - 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.

AB - 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.

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DO - 10.1109/CDC.2012.6426316

M3 - Conference contribution

SN - 9781467320665

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EP - 3537

BT - 2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

PB - Institute of Electrical and Electronics Engineers (IEEE)

ER -

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

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