Nonlinear System Identification by Haar Wavelets

?In order to precisely model real-life systems or man-made devices, both nonlinear and dynamic properties need to be taken into account. The generic, black-box model based on Volterra and Wiener serie

Block-oriented Nonlinear System Identification deals with an area of research that has been very active since the turn of the millennium. The book makes a pedagogical and cohesive presentation of the

The subject of the book is to present the modeling, parameter estimation and other aspects of the identification of nonlinear dynamic systems. The treatment is restricted to the input-output modeling

The book covers the most common and importantapproaches for the identification of nonlinear staticand dynamic systems. Additionally, it provides thereader with the necessary background on optimization

Presenting a thorough overview of the theoretical foundations of non-parametric system identification for nonlinear block-oriented systems, this book shows that non-parametric regression can be successfully applied to system identification, and it highlights the achievements in doing so. With emphasis on Hammerstein, Wiener systems, and their multidimensional extensions, the authors show how to identify nonlinear subsystems and their characteristics when limited information exists. Algorithms using trigonometric, Legendre, Laguerre, and Hermite series are investigated, and the kernel algorithm, its semirecursive versions, and fully recursive modifications are covered. The theories of modern non-parametric regression, approximation, and orthogonal expansions, along with new approaches to system identification (including semiparametric identification), are provided. Detailed information about all tools used is provided in the appendices. This book is for researchers and practitioners in

Presenting a thorough overview of the theoretical foundations of non-parametric system identification for nonlinear block-oriented systems, this book shows that non-parametric regression can be successfully applied to system identification, and it highlights the achievements in doing so. With emphasis on Hammerstein, Wiener systems, and their multidimensional extensions, the authors show how to identify nonlinear subsystems and their characteristics when limited information exists. Algorithms using trigonometric, Legendre, Laguerre, and Hermite series are investigated, and the kernel algorithm, its semirecursive versions, and fully recursive modifications are covered. The theories of modern non-parametric regression, approximation, and orthogonal expansions, along with new approaches to system identification (including semiparametric identification), are provided. Detailed information about all tools used is provided in the appendices. This book is for researchers and practitioners in

Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems

Jategaonkar provides a consolidated account of flight vehicle system identification that has evolved during recent decades, focusing particularly on nonlinear systems and the time-domain approach. He

This review volume reports the state-of-the-art in Linear Parameter Varying (LPV) system identification. Written by world renowned researchers, the book contains twelve chapters, focusing on the most

This text offers an excellent introduction to the mathematical theory of wavelets for senior undergraduate students. Despite the fact that this theory is intrinsically advanced, the author's elementary approach makes it accessible at the undergraduate level. Beginning with thorough accounts of inner product spaces and Hilbert spaces, the book then shifts its focus to wavelets specifically, starting with the Haar wavelet, broadening to wavelets in general, and culminating in the construction of the Daubechies wavelets. All of this is done using only elementary methods, bypassing the use of the Fourier integral transform. Arguments using the Fourier transform are introduced in the final chapter, and this less elementary approach is used to outline a second and quite different construction of the Daubechies wavelets. The main text of the book is supplemented by more than 200 exercises ranging in difficulty and complexity.

?This brief presents characterizations of identification errors under a probabilistic framework when output sensors are binary, quantized, or regular. By considering both space complexity in terms of

A textbook that grew out of a set of lecture notes prepared for a course on nonlinear system theory, given by the authors in 1988 to graduate students taking part in the Dutch national Graduate Progra

It is now widely recognized that the climate system is governed by nonlinear, multi-scale processes, whereby memory effects and stochastic forcing by fast processes, such as weather and convective systems, can induce regime behavior. Motivated by present difficulties in understanding the climate system and to aid the improvement of numerical weather and climate models, this book gathers contributions from mathematics, physics and climate science to highlight the latest developments and current research questions in nonlinear and stochastic climate dynamics. Leading researchers discuss some of the most challenging and exciting areas of research in the mathematical geosciences, such as the theory of tipping points and of extreme events including spatial extremes, climate networks, data assimilation and dynamical systems. This book provides graduate students and researchers with a broad overview of the physical climate system and introduces powerful data analysis and modeling methods for

A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probability, both in interpreting results and in the tools of analysis. This brilliant book, the first devoted to the area, develops this interplay between probability and analysis. After systematically presenting both analytic and probabilistic techniques, the author uses probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior. The book addresses the most fundamental questions in the theory of nonlinear Markov processes: existence, uniqueness, constructions, approximation schemes, regularity, law of large numbers and probabilistic interpretations. Its careful exposition makes the book accessible to researchers and grad

This book treats the topic of extending the adaptive filtering theory in the context of massive multichannel systems by taking into account a priori knowledge of the underlying system or signal. The s

This authoritative treatment covers theory, optimal estimation and a range of practical applications. The first book on the subject, and written by leading researchers, this clear and rigorous work presents a comprehensive theory for both the stability boundary and the stability regions of a range of nonlinear dynamical systems including continuous, discrete, complex, two-time-scale and non-hyperbolic systems, illustrated with numerical examples. The authors also propose new concepts of quasi-stability region and of relevant stability regions and their complete characterisations. Optimal schemes for estimating stability regions of general nonlinear dynamical systems are also covered, and finally the authors describe and explain how the theory is applied in applications including direct methods for power system transient stability analysis, nonlinear optimisation for finding a set of high-quality optimal solutions, stabilisation of nonlinear systems, ecosystem dynamics, and immunisation

Nature is inherently noisy and nonlinear. It is noisy in the sense that all macroscopic systems are subject to the fluctuations of their environments and also to internal fluctuations. It is nonlinear in the sense that the restoring force on a system displaced from equilibrium does not usually vary linearly with the size of the displacement. To calculate the properties of stochastic (noisy) nonlinear systems is in general extremely difficult, although considerable progress has been made in the past. The three volumes that make up Noise in Nonlinear Dynamical Systems comprise a collection of specially written authoritative reviews on all aspects of the subject, representative of all the major practitioners in the field. The third volume deals with experimental aspects of the study of noise in nonlinear dynamical systems. It covers noise-driven phenomena in superfluid helium, liquid crystals, lasers and optical bistability as well as the solution of stochastic equations by digital simula

Big Mechanisms in Systems Biology: Big Data Mining, Network Modeling, and Genome-Wide Data Identification explains big mechanisms of systems biology by system identification and big data mining method

Filtering and system identification are powerful techniques for building models of complex systems. This 2007 book discusses the design of reliable numerical methods to retrieve missing information in models derived using these techniques. Emphasis is on the least squares approach as applied to the linear state-space model, and problems of increasing complexity are analyzed and solved within this framework, starting with the Kalman filter and concluding with the estimation of a full model, noise statistics and state estimator directly from the data. Key background topics, including linear matrix algebra and linear system theory, are covered, followed by different estimation and identification methods in the state-space model. With end-of-chapter exercises, MATLAB simulations and numerous illustrations, this book will appeal to graduate students and researchers in electrical, mechanical and aerospace engineering. It is also useful for practitioners. Additional resources for this title,

Filtering and system identification are powerful techniques for building models of complex systems. This 2007 book discusses the design of reliable numerical methods to retrieve missing information in models derived using these techniques. Emphasis is on the least squares approach as applied to the linear state-space model, and problems of increasing complexity are analyzed and solved within this framework, starting with the Kalman filter and concluding with the estimation of a full model, noise statistics and state estimator directly from the data. Key background topics, including linear matrix algebra and linear system theory, are covered, followed by different estimation and identification methods in the state-space model. With end-of-chapter exercises, MATLAB simulations and numerous illustrations, this book will appeal to graduate students and researchers in electrical, mechanical and aerospace engineering. It is also useful for practitioners. Additional resources for this title,

Mathematical modelling of physiological systems promises to advance our understanding of complex biological phenomena and pathophysiology of diseases. In this book, the authors adopt a mathematical approach to characterize and explain the functioning of the gastrointestinal system. Using the mathematical foundations of thin shell theory, the authors patiently and comprehensively guide the reader through the fundamental theoretical concepts, via step-by-step derivations and mathematical exercises, from basic theory to complex physiological models. Applications to nonlinear problems related to the biomechanics of abdominal viscera and the theoretical limitations are discussed. Special attention is given to questions of complex geometry of organs, effects of boundary conditions on pellet propulsion, as well as to clinical conditions, e.g. functional dyspepsia, intestinal dysrhythmias and the effect of drugs to treat motility disorders. With end of chapter problems, this book is ideal for

In control theory, sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a nonlinear system by application of a discontinuous control signal that forces the system to “s

Contributors from various branches of science and engineering explore a class of nonlinear control systems resulting from the interaction of a control system with a system governed by the dynamics of

The recent appearance of wavelets as a new computational tool in applied mathematics has given a new impetus to the field of numerical analysis of Fredholm integral equations. This book gives an account of the state of the art in the study of fast multiscale methods for solving these equations based on wavelets. The authors begin by introducing essential concepts and describing conventional numerical methods. They then develop fast algorithms and apply these to solving linear, nonlinear Fredholm integral equations of the second kind, ill-posed integral equations of the first kind and eigen-problems of compact integral operators. Theorems of functional analysis used throughout the book are summarised in the appendix. The book is an essential reference for practitioners wishing to use the new techniques. It may also be used as a text, with the first five chapters forming the basis of a one-semester course for advanced undergraduates or beginning graduates.

Complexity increases with increasing system size in everything from organisms to organizations. The nonlinear dependence of a system’s functionality on its size, by means of an allometry relation, is

This book presents the performances of the computational method for system failure prediction by numerical analysis and nonlinear dynamic models. It includes the research of authors on the development

Presents a systematic view of vibro-impact dynamics based on the nonlinear dynamics analysisComprehensive understanding of any vibro-impact system is critically impeded by the lack of analytical tools

This book presents the nonlinear theory of continuum mechanics and demonstrates its use in developing nonlinear computer formulations for large displacement dynamic analysis. Basic concepts used in continuum mechanics are presented and used to develop nonlinear general finite element formulations that can be effectively used in large displacement analysis. The book considers two nonlinear finite element dynamic formulations: a general large deformation finite element formulation and a formulation that can efficiently solve small deformation problems that characterize very stiff structures. The book presents material clearly and systematically, assuming the reader has only basic knowledge in matrix and vector algebra and dynamics. The book is designed for use by advanced undergraduates and first-year graduate students. It is also a reference for researchers, practising engineers, and scientists working in computational mechanics, bio-mechanics, computational biology, multibody system dy

This book presents the nonlinear theory of continuum mechanics and demonstrates its use in developing nonlinear computer formulations for large displacement dynamic analysis. Basic concepts used in continuum mechanics are presented and used to develop nonlinear general finite element formulations that can be effectively used in large displacement analysis. The book considers two nonlinear finite element dynamic formulations: a general large deformation finite element formulation and a formulation that can efficiently solve small deformation problems that characterize very stiff structures. The book presents material clearly and systematically, assuming the reader has only basic knowledge in matrix and vector algebra and dynamics. The book is designed for use by advanced undergraduates and first-year graduate students. It is also a reference for researchers, practising engineers, and scientists working in computational mechanics, bio-mechanics, computational biology, multibody system dy

This book provides a comprehensive treatment of the Gross–Pitaevskii equation with a periodic potential; in particular, the localized modes supported by the periodic potential. It takes the mean-field model of the Bose–Einstein condensation as the starting point of analysis and addresses the existence and stability of localized modes. The mean-field model is simplified further to the coupled nonlinear Schrödinger equations, the nonlinear Dirac equations, and the discrete nonlinear Schrödinger equations. One of the important features of such systems is the existence of band gaps in the wave transmission spectra, which support stationary localized modes known as the gap solitons. These localized modes realise a balance between periodicity, dispersion and nonlinearity of the physical system. Written for researchers in applied mathematics, this book mainly focuses on the mathematical properties of the Gross–Pitaevskii equation. It also serves as a reference for theoretical physicists inter

Build high-performance, spectrally clean, energy-efficient mm-wave power amplifiers and transmitters with this cutting-edge guide to designing, modeling, analysing, implementing and testing new mm-wave systems. Suitable for students, researchers and practicing engineers, this self-contained guide provides in-depth coverage of state-of-the-art semiconductor devices and technologies, linear and nonlinear power amplifier technologies, efficient power combining systems, circuit concepts, system architectures and system-on-a-chip realizations. The world's foremost experts from industry and academia cover all aspects of the design process, from device technologies to system architectures. Accompanied by numerous case studies highlighting practical design techniques, tradeoffs and pitfalls, this is a superb resource for those working with high-frequency systems.

A tax expenditure is a 'tax break' allowed to a taxpayer or group of taxpayers, for example, by way of concession, deduction, deferral or exemption. The tax expenditure concept, as it was first identified, was designed to demonstrate the similarity between direct government spending on the one hand and spending through the tax system on the other. The identification of benefits provided through the tax system as tax expenditures allows analysts to consider the fiscal significance of those parts of the tax system which do not contribute to the primary purpose of raising revenue. Although a seemingly simple concept, it has generated a range of complex definitional and practical issues, and this book identifies and critically assesses the controversial aspects of tax expenditure and tax expenditure management.

This new edition explains how vibrations can be used in a broad spectrum of applications and how to meet the challenges faced by engineers and system designers. The text integrates linear and nonlinear systems, and covers the time domain and the frequency domain, responses to harmonic and transient excitations, and discrete and continuous system models. It focuses on modeling, analysis, prediction, and measurement to provide a complete understanding of the underlying physical vibratory phenomena and their relevance for engineering design. Knowledge is put into practice through numerous examples with real-world applications in a range of disciplines, detailed design guidelines applicable to various vibratory systems, and over forty online interactive graphics which provide a visual summary of system behaviors and enable students to carry out their own parametric studies. Some thirteen new tables act as a quick reference for self-study, detailing key characteristics of physical systems a

Extracting information from seismic data requires knowledge of seismic wave propagation and reflection. The commonly used method involves solving linearly for a reflectivity at every point within the Earth, but this book follows an alternative approach which invokes inverse scattering theory. By developing the theory of seismic imaging from basic principles, the authors relate the different models of seismic propagation, reflection and imaging - thus providing links to reflectivity-based imaging on the one hand and to nonlinear seismic inversion on the other. The comprehensive and physically complete linear imaging foundation developed presents new results at the leading edge of seismic processing for target location and identification. This book serves as a fundamental guide to seismic imaging principles and algorithms and their foundation in inverse scattering theory, and is a valuable resource for working geoscientists, scientific programmers and theoretical physicists.

Extracting information from seismic data requires knowledge of seismic wave propagation and reflection. The commonly used method involves solving linearly for a reflectivity at every point within the Earth, but this book follows an alternative approach which invokes inverse scattering theory. By developing the theory of seismic imaging from basic principles, the authors relate the different models of seismic propagation, reflection and imaging - thus providing links to reflectivity-based imaging on the one hand and to nonlinear seismic inversion on the other. The comprehensive and physically complete linear imaging foundation developed presents new results at the leading edge of seismic processing for target location and identification. This book serves as a fundamental guide to seismic imaging principles and algorithms and their foundation in inverse scattering theory, and is a valuable resource for working geoscientists, scientific programmers and theoretical physicists.

Certain nonlinear optimization problems arising in such disparate areas as the theory of computation, pure and applied probability and mathematical physics, can be solved by linear methods, provided one replaces the usual number system with one in which addition satisfies the idempotent law. This systematic study of the subject has emerged, triggered in part by a workshop organized by Hewlett-Packard's Basic Research Institute in the Mathematical Sciences (BRIMS), which brought together many leading researchers in the area. This volume is a record of that workshop, but it also includes other invited contributions, a broad Introduction to Idempotency, written specially for the book, and a bibliography of the subject. In sum, the articles cover both practical and more theoretical considerations, making it essential reading for all workers in the area.