Identifiability of Spatially-Varying and Constant Parameters in Distributed Systems of Parabolic Type

Abstract

For the parameter identification process to minimize the difference between the system output and the model output, this paper discusses the identifiability of spatially varying and constant parameters of the system described by a linear, 1-dimensional, parabolic partial differential equation. Only the parameters in the system equation (not in the boundary condition) are assumed to be unknown and the identifiability in the deterministic sense is treated. For both cases of distributed and pointwise measurements, several results for the parameter identifiability and nonidentifiability are obtained. As a result, the identifiability conditions depend on the profile of the state of the model for the case of the distributed measurement, while, for the case of the pointwise measurement, such conditions depend on the position of a detector and the form of initial or input functions. The results are represented in terms of a priori known quantities and are easily applied to practical problems.