TY - GEN

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

AU - Hofleitner, Aude

AU - Claudel, Christian G.

AU - Bayen, Alexandre M.

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2012/12

Y1 - 2012/12

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.

UR - http://hdl.handle.net/10754/575810

UR - http://ieeexplore.ieee.org/document/6426316/

UR - http://www.scopus.com/inward/record.url?scp=84874243480&partnerID=8YFLogxK

U2 - 10.1109/CDC.2012.6426316

DO - 10.1109/CDC.2012.6426316

M3 - Conference contribution

SN - 9781467320665

SP - 3531

EP - 3537

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

PB - Institute of Electrical and Electronics Engineers (IEEE)

ER -