Least Squares Methods for System Identification of Structured Models

Sammanfattning: The purpose of system identification is to build mathematical models for dynamical systems from experimental data. With the current increase in complexity of engineering systems, an important challenge is to develop accurate and computationally efficient algorithms.For estimation of parametric models, the prediction error method (PEM) is a benchmark in the field. When the noise is Gaussian and a quadratic cost function is used, PEM provides asymptotically efficient estimates if the model orders are correct. A disadvantage with PEM is that, in general, it requires minimizing a non-convex function. Alternative methods are then needed to provide initialization points for the optimization. Two important classes of such methods are subspace and instrumental variables.Other methods, such as Steiglitz-McBride, use iterative least squares to avoid the non-convexity of PEM. This thesis focuses on this class of methods, with the purpose of addressing common limitations in existing algorithms and suggesting more accurate and computationally efficient ones. In particular, the proposed methods first estimate a high order non-parametric model and then reduce this estimate to a model of lower order by iteratively applying least squares.Two methods are proposed. First, the weighted null-space fitting (WNSF) uses iterative weighted least squares to reduce the high order model to a parametric model of interest. Second, the model order reduction Steiglitz-McBride (MORSM) uses pre-filtering and Steiglitz-McBride to estimate a parametric model of the plant. The asymptotic properties of the methods are studied, which show that one iteration provides asymptotically efficient estimates. We also discuss two extensions for this type of methods: transient estimation and estimation of unstable systems.Simulation studies provide promising results regarding accuracy and convergence properties in comparison with PEM.