Multiple-Model Adaptive Observers for the Bio-Heat Equation With In-Domain Pointwise Outputs

The process of heat transfer in biological tissues is described by a parabolic partial differential equation, known as the Pennes’ bio-heat equation, which has the form of a heat equation with an affine reaction term. Handling adequately such equation is of paramount importance for the effectiveness of minimally invasive thermal therapies like, e.g., superficial hyperthermia. The control and estimation for the bio-heat equation are practically challenging due to the presence of uncertain diffusion and reaction coefficients, and to the fact that, typically, one can rely on pointwise measurements only. In this letter we address the problem by proposing an adaptive framework based on multiple-models building on a family of PDE observers together with a set of dynamic weights. The proposed techniques are general enough to be extended to other parabolic PDEs with unknown coefficients, thus going beyond the motivating setup of the bio-heat equation. Simulation examples support the theoretical findings.