Direct parameter identification of distributed parameter systems

A new direct approach to identifying the parameters of distributed parameter systems from noise-corrupted data is introduced. The model of the system which takes the form of a set of linear or nonlinear partial differential equations is assumed known with the exception of a set of constant parameters. Using finite-difference approximations of the spatial derivatives the original equation is transformed into a set of ordinary differential equations. The identification approach involves smoothing the measured data and estimating the temporal derivatives using a fixed interval smoother. A least-squares method is then employed to estimate the unknown parameters. Three examples that illustrate the applicability of the proposed approach are presented and discussed.