Observer Design with Sparsity for Parabolic PDEs

Abstract

Abstract This paper addresses a feasible way of constructing filter gains with sparsity in observer designs for parabolic PDEs. This topic is motivated by considerations of computational savings in optimal sensor placement, where a hybrid Domain Decomposition (DD) based filter for such problems is presented Demetriou (2018); Demetriou and Hu (2019). By decomposing the spatial domain into non-overlapping subdomains that some of them include sensors and the others do not, the resulting state estimators can employ different numerical grids to compute the associated filter gains. To implement the DD methods, it is key to understand the sparsity of the filter gains. In this work, a practical filter design based on the output measurement will be introduced. Moreover, rigorous analysis on the convergence of observation error is established.