Adaptive Estimation of the Pennes' Bio-Heat Equation - I: Observer Design

In this paper, we propose a multiple-model adaptive estimation setup for a class of uncertain parabolic reaction-diffusion PDEs encompassing the Pennes' bio-heat equation, which is a motivating case study from the perspective of biomedical applications such as hyperthermia. The efficacy of the approach in estimating the system solution and recovering the value of the reaction coefficient is validated through numerical simulations in MATLAB. The validation step has highlited some limitations of classical numerical simulation tools that we propose to handle through an implementation of the estimator relying on Deep Learning libraries. This alternative approach is reported in a companion paper (Part II of this work).