Identification of Finite-dimensional Models for Distributed-parameter Systems

This paper addresses the problem of obtaining finite dimensional models of distributedparameter systems from measurement data using system identification. The data are used to construct approximations of the solution and the forcing function in a finite dimensional space, which are expressed in terms of a finite element basis. A discrete time model is then identified based on the resulting finite dimensional coordinate vector. The existence and convergence of such a representation is established for a class of abstract first order systems. The proposed approach is illustrated in practice using simulated noise contaminated data.