State and parameter estimation in 1-D hyperbolic PDEs based on an adjoint method
Résumé
An optimal estimation method for state and distributed parameters in
1-D hyperbolic system based on adjoint method is proposed in this
paper. A general form of the partial differential equations governing
the dynamics of system is first introduced. In this equation, the
initial condition or state variable as well as some empirical
parameters are supposed to be unknown and need to be estimated. The
Lagrangian multiplier method is used to connect the dynamics of the
system and the cost function defined as the least square error between
the simulation values and the measurements. The adjoint state method is
applied to the objective functional in order to get the adjoint system
and the gradients with respect to parameters and initial state. The
objective functional is minimized by Broyden–Fletcher–Goldfarb–Shanno
(BFGS) method. Due to the non-linearity of both direct and adjoint
system, the nonlinear explicit Lax–Wendroff scheme is used to solve
them numerically. The presented optimal estimation approach is
validated by two illustrative examples, the first one about state and
parameter estimation in a traffic flow, and the second one in an
overland flow system.
Domaines
Automatique / Robotique
Origine : Fichiers produits par l'(les) auteur(s)
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