On reduced order observer for radiative conductive heat transfer systems

This contribution deals with state observer design for a class of PDE non linear systems described by Radiative transfer equation (RTE) coupled with nonlinear heat equation (NHE) in two dimensional domain. Observations are made though sensors placed at the upper boundary of the two dimensional domain. We explored the Galerkin method for a semi-discretization to obtain a large scale in finite dimensional. Thanks to the special structure of the obtained state system, we show through the Differential Mean Value Theorem (DMVT) that there always exists an observer gain matrix that assures asymptotic convergence. Both full order and reduced order state estimators are provided.