Identifiability and Determination of Unknown Functions for a Class of Distributed Parameter Systems

Abstract

In this paper the identifiability and the problem of determination of unknown functions are investigated for a class of distributed parameter systems. In a distributed parameter system, the identifiability of the system is a sufficient condition for the unknown function to be uniquely determined from the measurement data, but is not a sufficient condition for the function to depend continuously on the measurement data. The problem of the unknown-function determination is not generally well-posed for a distributed parameter system. In this paper a well-posed approximating method is presented for the unknown-function determination. This method gives an approximate function depending continuously on the measurement data. The necessary and sufficient condition for identifiability is also presented for a class of distributed parameter systems.