Title :
Adaptive space-time distributed parameter and input estimation in heat transport with unknown bounds
Author :
Mechhoud, Sarah ; Witrant, Emmanuel ; Dugard, Luc
Author_Institution :
Grenoble Image Parole Signal Autom. (GIPSA-Lab.), UJFGrenoble, St. Martin d´Hères, France
Abstract :
In this paper, we discuss on-line adaptive estimation of distributed diffusion and source term coefficients for a non-homogeneous linear parabolic partial differential equation describing heat transport. An estimator is defined in the infinite-dimensional framework having the system state and the parameters´ estimate as its states. Our scheme allows to estimate spatially distributed and space-time distributed parameters. While the parameters convergence depends on the plant signal richness assumption, the state convergence is established using the Lyapunov approach. Since the estimator is infinite-dimensional, the b-splines Galerkin finite element method is used to implement it. In silico simulations are provided to illustrate the performance of the proposed approach.
Keywords :
Galerkin method; convergence of numerical methods; finite element analysis; heat transfer; linear differential equations; parabolic equations; parameter estimation; partial differential equations; splines (mathematics); Lyapunov approach; adaptive space-time distributed parameter; b-splines Galerkin finite element method; distributed diffusion; heat transport; in-silico simulations; infinite-dimensional estimator; input estimation; nonhomogeneous linear parabolic partial differential equation; online adaptive estimation; parameter convergence; source term coefficients; space-time distributed parameter estimation; spatially distributed parameter estimation; system state convergence; unknown bounds; Adaptation models; Adaptive estimation; Boundary conditions; Convergence; Estimation; Heating; Mathematical model;
Conference_Titel :
Systems and Control (ICSC), 2013 3rd International Conference on
Conference_Location :
Algiers
Print_ISBN :
978-1-4799-0273-6
DOI :
10.1109/ICoSC.2013.6750931