Adaptive Learning Methods for Nonlinear System Modeling


Book Description

Adaptive Learning Methods for Nonlinear System Modeling presents some of the recent advances on adaptive algorithms and machine learning methods designed for nonlinear system modeling and identification. Real-life problems always entail a certain degree of nonlinearity, which makes linear models a non-optimal choice. This book mainly focuses on those methodologies for nonlinear modeling that involve any adaptive learning approaches to process data coming from an unknown nonlinear system. By learning from available data, such methods aim at estimating the nonlinearity introduced by the unknown system. In particular, the methods presented in this book are based on online learning approaches, which process the data example-by-example and allow to model even complex nonlinearities, e.g., showing time-varying and dynamic behaviors. Possible fields of applications of such algorithms includes distributed sensor networks, wireless communications, channel identification, predictive maintenance, wind prediction, network security, vehicular networks, active noise control, information forensics and security, tracking control in mobile robots, power systems, and nonlinear modeling in big data, among many others. This book serves as a crucial resource for researchers, PhD and post-graduate students working in the areas of machine learning, signal processing, adaptive filtering, nonlinear control, system identification, cooperative systems, computational intelligence. This book may be also of interest to the industry market and practitioners working with a wide variety of nonlinear systems. Presents the key trends and future perspectives in the field of nonlinear signal processing and adaptive learning. Introduces novel solutions and improvements over the state-of-the-art methods in the very exciting area of online and adaptive nonlinear identification. Helps readers understand important methods that are effective in nonlinear system modelling, suggesting the right methodology to address particular issues.




Artificial Neural Networks for Modelling and Control of Non-Linear Systems


Book Description

Artificial neural networks possess several properties that make them particularly attractive for applications to modelling and control of complex non-linear systems. Among these properties are their universal approximation ability, their parallel network structure and the availability of on- and off-line learning methods for the interconnection weights. However, dynamic models that contain neural network architectures might be highly non-linear and difficult to analyse as a result. Artificial Neural Networks for Modelling and Control of Non-Linear Systems investigates the subject from a system theoretical point of view. However the mathematical theory that is required from the reader is limited to matrix calculus, basic analysis, differential equations and basic linear system theory. No preliminary knowledge of neural networks is explicitly required. The book presents both classical and novel network architectures and learning algorithms for modelling and control. Topics include non-linear system identification, neural optimal control, top-down model based neural control design and stability analysis of neural control systems. A major contribution of this book is to introduce NLq Theory as an extension towards modern control theory, in order to analyze and synthesize non-linear systems that contain linear together with static non-linear operators that satisfy a sector condition: neural state space control systems are an example. Moreover, it turns out that NLq Theory is unifying with respect to many problems arising in neural networks, systems and control. Examples show that complex non-linear systems can be modelled and controlled within NLq theory, including mastering chaos. The didactic flavor of this book makes it suitable for use as a text for a course on Neural Networks. In addition, researchers and designers will find many important new techniques, in particular NLq emTheory, that have applications in control theory, system theory, circuit theory and Time Series Analysis.




Sampled-Data Models for Linear and Nonlinear Systems


Book Description

Sampled-data Models for Linear and Nonlinear Systems provides a fresh new look at a subject with which many researchers may think themselves familiar. Rather than emphasising the differences between sampled-data and continuous-time systems, the authors proceed from the premise that, with modern sampling rates being as high as they are, it is becoming more appropriate to emphasise connections and similarities. The text is driven by three motives: · the ubiquity of computers in modern control and signal-processing equipment means that sampling of systems that really evolve continuously is unavoidable; · although superficially straightforward, sampling can easily produce erroneous results when not treated properly; and · the need for a thorough understanding of many aspects of sampling among researchers and engineers dealing with applications to which they are central. The authors tackle many misconceptions which, although appearing reasonable at first sight, are in fact either partially or completely erroneous. They also deal with linear and nonlinear, deterministic and stochastic cases. The impact of the ideas presented on several standard problems in signals and systems is illustrated using a number of applications. Academic researchers and graduate students in systems, control and signal processing will find the ideas presented in Sampled-data Models for Linear and Nonlinear Systems to be a useful manual for dealing with sampled-data systems, clearing away mistaken ideas and bringing the subject thoroughly up to date. Researchers in statistics and economics will also derive benefit from the reworking of ideas relating a model derived from data sampling to an original continuous system.







Nonlinear Modeling


Book Description

This collection of eight contributions presents advanced black-box techniques for nonlinear modeling. The methods discussed include neural nets and related model structures for nonlinear system identification, enhanced multi-stream Kalman filter training for recurrent networks, the support vector method of function estimation, parametric density estimation for the classification of acoustic feature vectors in speech recognition, wavelet based modeling of nonlinear systems, nonlinear identification based on fuzzy models, statistical learning in control and matrix theory, and nonlinear time- series analysis. The volume concludes with the results of a time- series prediction competition held at a July 1998 workshop in Belgium. Annotation copyrighted by Book News, Inc., Portland, OR.




Nonlinear Systems


Book Description

This book focuses on several key aspects of nonlinear systems including dynamic modeling, state estimation, and stability analysis. It is intended to provide a wide range of readers in applied mathematics and various engineering disciplines an excellent survey of recent studies of nonlinear systems. With its thirteen chapters, the book brings together important contributions from renowned international researchers to provide an excellent survey of recent studies of nonlinear systems. The first section consists of eight chapters that focus on nonlinear dynamic modeling and analysis techniques, while the next section is composed of five chapters that center on state estimation methods and stability analysis for nonlinear systems.




Linear and Nonlinear System Modeling


Book Description

Written and edited by a team of experts in the field, this exciting new volume presents the cutting-edge techniques, latest trends, and state-of-the-art practical applications in linear and nonlinear system modeling. Mathematical modeling of control systems is, essentially, extracting the essence of practical problems into systematic mathematical language. In system modeling, mathematical expression deals with modeling and its applications. It is characterized that how a modeling competency can be categorized and its activity can contribute to building up these competencies. Mathematical modeling of a practical system is an attractive field of research and an advanced subject with a variety of applications. The main objective of mathematical modeling is to predict the behavior of the system under different operating conditions and to design and implement efficient control strategies to achieve the desired performance. A considerable effort has been directed to the development of models, which must be understandable and easy to analyze. It is a very difficult task to develop mathematical modeling of complicated practical systems considering all its possible high-level non-linearity and cross couple dynamics. Although mathematical modeling of nonlinear systems sounds quite interesting, it is difficult to formulate the general solution to analyze and synthesize nonlinear dynamical systems. Most of the natural processes are nonlinear, having very high computational complexity of several numerical issues. It is impossible to create any general solution or individual procedure to develop exact modeling of a non-linear system, which is often improper and too complex for engineering practices. Therefore, some series of approximation procedures are used, in order to get some necessary knowledge about the nonlinear system dynamics. There are several complicated mathematical approaches for solving these types of problems, such as functional analysis, differential geometry or the theory of nonlinear differential equations.




Linear and Nonlinear System Modelling


Book Description

Mathematical modelling of control systems is, essentially, extracting the essence of practical problems into systematic mathematical language. In system modelling, mathematical expression deals with modelling and its applications. It is characterized that how a modelling competency can be categorized and its activity can contribute to building up these competencies. Mathematical modelling of a practical system is an attractive field of research and an advanced subject with a variety of applications. The main objective of mathematical modelling is to predict the behavior of the system under different operating conditions and to design and implement efficient control strategies to achieve the desired performance. A considerable effort has been directed to the development of models, which must be understandable and easy to analyze. It is a very difficult task to develop mathematical modelling of complicated practical systems considering all its possible high-level non-linearity and cross couple dynamics. Although mathematical modelling of nonlinear systems sounds quite interesting, it is difficult to formulate the general solution to analyze and synthesize nonlinear dynamical systems. Most of the natural processes are nonlinear, having very high computational complexity of several numerical issues. It is impossible to create any general solution or individual procedure to develop exact modeling of a non-linear system, which is often improper and too complex for engineering practices. Therefore, some series of approximation procedures are used, in order to get some necessary knowledge about the nonlinear system dynamics. There are several complicated mathematical approaches for solving these types of problems, such as functional analysis, differential geometry or the theory of nonlinear differential equations. This book covers these issues and offers real-world practical solutions for everyday problems encountered by engineers and scientists. Whether for the veteran engineer, scientist in the lab, student, or faculty, this groundbreaking new volume is a valuable resource for researchers and other industry professionals interested in the intersection of mathematical modeling and control systems.




Nonlinear System Identification


Book Description

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 in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice. Includes coverage of: The NARMAX (nonlinear autoregressive moving average with exogenous inputs) model The orthogonal least squares algorithm that allows models to be built term by term where the error reduction ratio reveals the percentage contribution of each model term Statistical and qualitative model validation methods that can be applied to any model class Generalised frequency response functions which provide significant insight into nonlinear behaviours A completely new class of filters that can move, split, spread, and focus energy The response spectrum map and the study of sub harmonic and severely nonlinear systems Algorithms that can track rapid time variation in both linear and nonlinear systems The important class of spatio-temporal systems that evolve over both space and time Many case study examples from modelling space weather, through identification of a model of the visual processing system of fruit flies, to tracking causality in EEG data are all included to demonstrate how easily the methods can be applied in practice and to show the insight that the algorithms reveal even for complex systems NARMAX algorithms provide a fundamentally different approach to nonlinear system identification and signal processing for nonlinear systems. NARMAX methods provide models that are transparent, which can easily be analysed, and which can be used to solve real problems. This book is intended for graduates, postgraduates and researchers in the sciences and engineering, and also for users from other fields who have collected data and who wish to identify models to help to understand the dynamics of their systems.




Adaptive Nonlinear System Identification


Book Description

Focuses on System Identification applications of the adaptive methods presented. but which can also be applied to other applications of adaptive nonlinear processes. Covers recent research results in the area of adaptive nonlinear system identification from the authors and other researchers in the field.