Identifiability Of State Space Models

Statistical and mathematical models are defined by parameters that describe different characteristics of those models. Ideally it would be possible to find parameter estimates for every parameter in that model, but, in some cases, this is not possible. For example, two parameters that only ever appear in the model as a product could not be estimated individually; only the product can be estimated. Such a model is said to be parameter redundant, or the parameters are described as non-identifiable. This book explains why parameter redundancy and non-identifiability is a problem and the different methods that can be used for detection, including in a Bayesian context. Key features of this book: Detailed discussion of the problems caused by parameter redundancy and non-identifiability Explanation of the different general methods for detecting parameter redundancy and non-identifiability, including symbolic algebra and numerical methods Chapter on Bayesian identifiability Throughout illustrative examples are used to clearly demonstrate each problem and method. Maple and R code are available for these examples More in-depth focus on the areas of discrete and continuous state-space models and ecological statistics, including methods that have been specifically developed for each of these areas This book is designed to make parameter redundancy and non-identifiability accessible and understandable to a wide audience from masters and PhD students to researchers, from mathematicians and statisticians to practitioners using mathematical or statistical models.

Master Techniques and Successfully Build Models Using a Single Resource Vital to all data-driven or measurement-based process operations, system identification is an interface that is based on observational science, and centers on developing mathematical models from observed data. Principles of System Identification: Theory and Practice is an introductory-level book that presents the basic foundations and underlying methods relevant to system identification. The overall scope of the book focuses on system identification with an emphasis on practice, and concentrates most specifically on discrete-time linear system identification. Useful for Both Theory and Practice The book presents the foundational pillars of identification, namely, the theory of discrete-time LTI systems, the basics of signal processing, the theory of random processes, and estimation theory. It explains the core theoretical concepts of building (linear) dynamic models from experimental data, as well as the experimental and practical aspects of identification. The author offers glimpses of modern developments in this area, and provides numerical and simulation-based examples, case studies, end-of-chapter problems, and other ample references to code for illustration and training. Comprising 26 chapters, and ideal for coursework and self-study, this extensive text: Provides the essential concepts of identification Lays down the foundations of mathematical descriptions of systems, random processes, and estimation in the context of identification Discusses the theory pertaining to non-parametric and parametric models for deterministic-plus-stochastic LTI systems in detail Demonstrates the concepts and methods of identification on different case-studies Presents a gradual development of state-space identification and grey-box modeling Offers an overview of advanced topics of identification namely the linear time-varying (LTV), non-linear, and closed-loop identification Discusses a multivariable approach to identification using the iterative principal component analysis Embeds MATLAB® codes for illustrated examples in the text at the respective points Principles of System Identification: Theory and Practice presents a formal base in LTI deterministic and stochastic systems modeling and estimation theory; it is a one-stop reference for introductory to moderately advanced courses on system identification, as well as introductory courses on stochastic signal processing or time-series analysis.The MATLAB scripts and SIMULINK models used as examples and case studies in the book are also available on the author's website: http://arunkt.wix.com/homepage#!textbook/c397

Identifiability of Parametric Models provides a comprehensive presentation of identifiability. This book is divided into 11 chapters. Chapter 1 reviews the basic methods for structural identifiability testing. The methods that deal with large-scale models and propose conjectures on global identifiability are considered in Chapter 2, while the problems of initial model selection and generating the set of models that have the exact same input-output behavior are evaluated in Chapter 3. Chapters 4 and 5 cover nonlinear models. The relations between identifiability and the well-posedness of the estimation problem are analyzed in Chapter 6, followed by a description of the algebraic manipulations required for testing a model for structural controllability, observability, identifiability, or distinguishability in chapter 7. The rest of the chapters are devoted to the relations between identifiability and parameter uncertainty. This publication is beneficial to students and researchers aiming to acquire knowledge of the identifiability of parametric models.

This book is dedicated to Prof. Peter Young on his 70th birthday. Professor Young has been a pioneer in systems and control, and over the past 45 years he has influenced many developments in this field. This volume comprises a collection of contributions by leading experts in system identification, time-series analysis, environmetric modelling and control system design – modern research in topics that reflect important areas of interest in Professor Young’s research career. Recent theoretical developments in and relevant applications of these areas are explored treating the various subjects broadly and in depth. The authoritative and up-to-date research presented here will be of interest to academic researcher in control and disciplines related to environmental research, particularly those to with water systems. The tutorial style in which many of the contributions are composed also makes the book suitable as a source of study material for graduate students in those areas.