System Identification

This book on linear system identification contains twelve chapters and two appendices with Chapter 1 (Introduction) devoted to a general motivation by means of application examples from engineering and science.Chapter 2 (Introductory Examples) contains a presentation of four aspects or factors affecting identification, i.e., the system, the model structure, the identification method and the experimental condition.A traditional but not very clear distinction is here being made between nonparametric methods (transient analysis and correlation analysis) and parametric methods adapted to linear models.Problems of bias and consistency are discussed in a traditional manner and followed by experimental issues in the form of excitation and complications due to feedback control.Chapter 3 (Nonparametric Methods) deals with a short treatment covering transient analysis, frequency (response) analysis, correlation analysis, and spectral analysis.Chapter 4 (Linear Regression) with a presentation of the least-squares method and the normal equations including statistical and computational aspects as applied to estimation of system parameters.In Chapter 5 (Input Signals) is being characterized what is an appropriate input to a system under investigation.Spectral and statistical properties such as persistency of excitation are covered.Chapter 6 (Model Parametrizations) contains a classification of various types of discrete-time linear input-output models with a discussion on uniqueness and identifiability.Little attention is given to multivariable systems.Chapter 7 (Prediction Error Methods) contains a framework aiming to assess identification as a mathematical problem related to the Kolmogorov-Wiener approaches to linear prediction.Statistical properties of least-squares methods and the maximum-likelihood method are treated with some detail for Gaussian noise processes.This chapter appears to be the main chapter of the book.Chapter 8 (Instrumental Variable Methods) treats a number of modifications to the least-squares method.Several algorithms usually presented in their own right such as the Yule-Walker equations or the Levinson-Durbin algorithm are here considered in the framework of instrumental methods.Chapter 9 (Recursive Identification Methods) is introduced as a special computational organization of least-squares estimation and the correspondence with the Kalman filter is demonstrated.Several different recursive identification methods are presented.In Chapter 10 (Identification of Systems Operating in Closed Loop) is considered the problems appearing when the system input is generated by a feedback loop.