Adaptive space-time distributed parameter and input estimation in heat transport with unknown bounds

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.