## Introduction to Mathematical Systems Theory

*Linear Systems, Identification and Control*

**Author**: Christiaan Heij,André C.M. Ran,F. van Schagen

**Publisher:**Springer Science & Business Media

**ISBN:**3764375493

**Category:**Science

**Page:**166

**View:**2097

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This book provides an introduction to the theory of linear systems and control for students in business mathematics, econometrics, computer science, and engineering; the focus is on discrete time systems. The subjects treated are among the central topics of deterministic linear system theory: controllability, observability, realization theory, stability and stabilization by feedback, LQ-optimal control theory. Kalman filtering and LQC-control of stochastic systems are also discussed, as are modeling, time series analysis and model specification, along with model validation.

## Identification of Dynamic Systems

*An Introduction with Applications*

**Author**: Rolf Isermann,Marco Münchhof

**Publisher:**Springer Science & Business Media

**ISBN:**9783540788799

**Category:**Technology & Engineering

**Page:**705

**View:**3917

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Precise dynamic models of processes are required for many applications, ranging from control engineering to the natural sciences and economics. Frequently, such precise models cannot be derived using theoretical considerations alone. Therefore, they must be determined experimentally. This book treats the determination of dynamic models based on measurements taken at the process, which is known as system identification or process identification. Both offline and online methods are presented, i.e. methods that post-process the measured data as well as methods that provide models during the measurement. The book is theory-oriented and application-oriented and most methods covered have been used successfully in practical applications for many different processes. Illustrative examples in this book with real measured data range from hydraulic and electric actuators up to combustion engines. Real experimental data is also provided on the Springer webpage, allowing readers to gather their first experience with the methods presented in this book. Among others, the book covers the following subjects: determination of the non-parametric frequency response, (fast) Fourier transform, correlation analysis, parameter estimation with a focus on the method of Least Squares and modifications, identification of time-variant processes, identification in closed-loop, identification of continuous time processes, and subspace methods. Some methods for nonlinear system identification are also considered, such as the Extended Kalman filter and neural networks. The different methods are compared by using a real three-mass oscillator process, a model of a drive train. For many identification methods, hints for the practical implementation and application are provided. The book is intended to meet the needs of students and practicing engineers working in research and development, design and manufacturing.

## System Identification

*An Introduction*

**Author**: Karel J. Keesman

**Publisher:**Springer Science & Business Media

**ISBN:**9780857295224

**Category:**Technology & Engineering

**Page:**323

**View:**5007

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System Identification shows the student reader how to approach the system identification problem in a systematic fashion. The process is divided into three basic steps: experimental design and data collection; model structure selection and parameter estimation; and model validation, each of which is the subject of one or more parts of the text. Following an introduction on system theory, particularly in relation to model representation and model properties, the book contains four parts covering: • data-based identification – non-parametric methods for use when prior system knowledge is very limited; • time-invariant identification for systems with constant parameters; • time-varying systems identification, primarily with recursive estimation techniques; and • model validation methods. A fifth part, composed of appendices, covers the various aspects of the underlying mathematics needed to begin using the text. The book uses essentially semi-physical or gray-box modeling methods although data-based, transfer-function system descriptions are also introduced. The approach is problem-based rather than rigorously mathematical. The use of finite input–output data is demonstrated for frequency- and time-domain identification in static, dynamic, linear, nonlinear, time-invariant and time-varying systems. Simple examples are used to show readers how to perform and emulate the identification steps involved in various control design methods with more complex illustrations derived from real physical, chemical and biological applications being used to demonstrate the practical applicability of the methods described. End-of-chapter exercises (for which a downloadable instructors’ Solutions Manual is available from fill in URL here) will both help students to assimilate what they have learned and make the book suitable for self-tuition by practitioners looking to brush up on modern techniques. Graduate and final-year undergraduate students will find this text to be a practical and realistic course in system identification that can be used for assessing the processes of a variety of engineering disciplines. System Identification will help academic instructors teaching control-related to give their students a good understanding of identification methods that can be used in the real world without the encumbrance of undue mathematical detail.

## Die Erforschung des Chaos

*Eine Einführung für Naturwissenschaftler und Ingenieure*

**Author**: John H. Argyris,Gunter Faust,Maria Haase

**Publisher:**Springer-Verlag

**ISBN:**3322904415

**Category:**Mathematics

**Page:**790

**View:**4805

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Das Buch stellt die grundlegenden Konzepte der Chaos-Theorie und die mathematischen Hilfsmittel so elementar wie möglich dar.

## Linear Operators and Linear Systems

*An Analytical Approach to Control Theory*

**Author**: Jonathan R. Partington,C. M. Series

**Publisher:**Cambridge University Press

**ISBN:**9780521546195

**Category:**Mathematics

**Page:**166

**View:**1304

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"Suitable for students of analysis, this book also acts as an introduction to a mathematical approach to systems and control for graduate students in departments of applied mathematics or engineering."--Jacket.

## Intelligent Control Systems Using Computational Intelligence Techniques

**Author**: A.E. Ruano

**Publisher:**IET

**ISBN:**9780863414893

**Category:**Computers

**Page:**454

**View:**8173

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Intelligent Control techniques are becoming important tools in both academia and industry. Methodologies developed in the field of soft-computing, such as neural networks, fuzzy systems and evolutionary computation, can lead to accommodation of more complex processes, improved performance and considerable time savings and cost reductions. Intelligent Control Systems using Computational Intellingence Techniques details the application of these tools to the field of control systems. Each chapter gives and overview of current approaches in the topic covered, with a set of the most important references in the field, and then details the author's approach, examining both the theory and practical applications.

## Wave Motion, Intelligent Structures and Nonlinear Mechanics

*A Herbert berall Festschrift Volume*

**Author**: Herbert berall,Ardshir Guran,D. J. Inman

**Publisher:**World Scientific

**ISBN:**9789810229818

**Category:**Science

**Page:**301

**View:**4430

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This book is a collection of papers on the subject of applied system dynamics and control written by experts in this field. It offers the reader a sampling of exciting research areas in three fast-growing branches: (i) Wave Motion (ii) Intelligent Structures (iii) Nonlinear Mechanics. The topics covered include flow instability, nonlinear mode localization autoparametric systems with pendula, and geometric stiffening in multibody dynamics. Mathematical methods include perturbation methods, modern control theory, nonlinear neural nets, and resonance scattering theory of berall-Ripoche-Maze. Applications include sound-induced structural vibrations, fiber acoustic waveguides, vibration suppression of structures, linear control of gyroscopic systems, and nonlinear control of distributed systems.This book shows how applied system dynamics and control is currently being utilized and investigated. It will be of interest to engineers, applied mathematicians and physicists.

## Discrete-Time Linear Systems

*Theory and Design with Applications*

**Author**: Guoxiang Gu

**Publisher:**Springer Science & Business Media

**ISBN:**1461422817

**Category:**Technology & Engineering

**Page:**452

**View:**3886

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Discrete-Time Linear Systems: Theory and Design with Applications combines system theory and design in order to show the importance of system theory and its role in system design. The book focuses on system theory (including optimal state feedback and optimal state estimation) and system design (with applications to feedback control systems and wireless transceivers, plus system identification and channel estimation).

## Operators, Systems and Linear Algebra

*Three Decades of Algebraic Systems Theory*

**Author**: Dieter Prätzel-Wolters,Eva Zerz

**Publisher:**Springer-Verlag

**ISBN:**3663098230

**Category:**Technology & Engineering

**Page:**224

**View:**5547

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## An Introduction to Infinite-Dimensional Linear Systems Theory

**Author**: Ruth F. Curtain,Hans Zwart

**Publisher:**Springer Science & Business Media

**ISBN:**9780387944753

**Category:**Mathematics

**Page:**698

**View:**1191

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Infinite dimensional systems is now an established area of research. Given the recent trend in systems theory and in applications towards a synthesis of time- and frequency-domain methods, there is a need for an introductory text which treats both state-space and frequency-domain aspects in an integrated fashion. The authors' primary aim is to write an introductory textbook for a course on infinite dimensional linear systems. An important consideration by the authors is that their book should be accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Consequently, all the mathematical background is summarized in an extensive appendix. For the majority of students, this would be their only acquaintance with infinite dimensional systems.

## Mathematics of Complexity and Dynamical Systems

**Author**: Robert A. Meyers

**Publisher:**Springer Science & Business Media

**ISBN:**1461418054

**Category:**Mathematics

**Page:**1858

**View:**9871

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Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

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

**Author**: Johan A.K. Suykens,Joos P.L. Vandewalle,B.L. de Moor

**Publisher:**Springer Science & Business Media

**ISBN:**1475724934

**Category:**Technology & Engineering

**Page:**235

**View:**844

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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.

## System Identification (SYSID '03)

*A Proceedings Volume from the 13th IFAC Symposium on System Identification, Rotterdam, the Netherlands, 27-29 August 2003*

**Author**: P. M. J. van den Hof,Bo Wahlberg,Siep Weiland

**Publisher:**Elsevier

**ISBN:**9780080437095

**Category:**Science

**Page:**1984

**View:**7197

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The scope of the symposium covers all major aspects of system identification, experimental modelling, signal processing and adaptive control, ranging from theoretical, methodological and scientific developments to a large variety of (engineering) application areas. It is the intention of the organizers to promote SYSID 2003 as a meeting place where scientists and engineers from several research communities can meet to discuss issues related to these areas. Relevant topics for the symposium program include: Identification of linear and multivariable systems, identification of nonlinear systems, including neural networks, identification of hybrid and distributed systems, Identification for control, experimental modelling in process control, vibration and modal analysis, model validation, monitoring and fault detection, signal processing and communication, parameter estimation and inverse modelling, statistical analysis and uncertainty bounding, adaptive control and data-based controller tuning, learning, data mining and Bayesian approaches, sequential Monte Carlo methods, including particle filtering, applications in process control systems, motion control systems, robotics, aerospace systems, bioengineering and medical systems, physical measurement systems, automotive systems, econometrics, transportation and communication systems *Provides the latest research on System Identification *Contains contributions written by experts in the field *Part of the IFAC Proceedings Series which provides a comprehensive overview of the major topics in control engineering.

## Neural Networks for Control

**Author**: W. Thomas Miller,Paul J. Werbos,Richard S. Sutton

**Publisher:**MIT Press

**ISBN:**9780262631617

**Category:**Psychology

**Page:**544

**View:**2790

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Neural Networks for Control highlights key issues in learning control and identifiesresearch directions that could lead to practical solutions for control problems in criticalapplication domains. It addresses general issues of neural network based control and neural networklearning with regard to specific problems of motion planning and control in robotics, and takes upapplication domains well suited to the capabilities of neural network controllers. The appendixdescribes seven benchmark control problems.W. Thomas Miller, III is Professor of Electrical andComputer Engineering at the University of New Hampshire. Richard S. Sutton works for GTELaboratories Incorporated. Paul J. Werbos is Program Director for Neuroengineering at the NationalScience Foundation.Contributors: Andrew G. Barto. Ronald J. Williams. Paul J. Werbos. Kumpati S.Narendra. L. Gordon Kraft, III, David P. Campagna. Mitsuo Kawato. Bartlett W. Met. Christopher G.Atkeson, David J. Reinkensmeyer. Derrick Nguyen, Bernard Widrow. James C. Houk, Satinder P. Singh,Charles Fisher. Judy A. Franklin, Oliver G. Selfridge. Arthur C. Sanderson. Lyle H. Ungar. CharlesC. Jorgensen, C. Schley. Martin Herman, James S. Albus, Tsai-Hong Hong. Charles W. Anderson, W.Thomas Miller, III.

## Modeling and Identification of Linear Parameter-Varying Systems

**Author**: Roland Toth

**Publisher:**Springer Science & Business Media

**ISBN:**364213811X

**Category:**Technology & Engineering

**Page:**325

**View:**1353

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Through the past 20 years, the framework of Linear Parameter-Varying (LPV) systems has become a promising system theoretical approach to h- dle the controlof mildly nonlinear and especially position dependent systems which are common in mechatronic applications and in the process ind- try. The birth of this system class was initiated by the need of engineers to achieve better performance for nonlinear and time-varying dynamics, c- mon in many industrial applications, than what the classical framework of Linear Time-Invariant (LTI) control can provide. However, it was also a p- mary goal to preserve simplicity and “re-use” the powerful LTI results by extending them to the LPV case. The progress continued according to this philosophy and LPV control has become a well established ?eld with many promising applications. Unfortunately, modeling of LPV systems, especially based on measured data (which is called system identi?cation) has seen a limited development sincethebirthoftheframework. Currentlythisbottleneck oftheLPVfra- work is halting the transfer of the LPV theory into industrial use. Without good models that ful?ll the expectations of the users and without the und- standing how these models correspond to the dynamics of the application, it is di?cult to design high performance LPV control solutions. This book aims to bridge the gap between modeling and control by investigating the fundamental questions of LPV modeling and identi?cation. It explores the missing details of the LPV system theory that have hindered the formu- tion of a well established identi?cation framework.

## Algebraic Identification and Estimation Methods in Feedback Control Systems

**Author**: Hebertt Sira-Ramírez,Carlos García Rodríguez,John Cortés Romero,Alberto Luviano Juárez

**Publisher:**John Wiley & Sons

**ISBN:**1118730585

**Category:**Technology & Engineering

**Page:**392

**View:**3794

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Algebraic Identification and Estimation Methods in FeedbackControl Systems presents a model-based algebraic approach toonline parameter and state estimation in uncertain dynamic feedbackcontrol systems. This approach evades the mathematical intricaciesof the traditional stochastic approach, proposing a directmodel-based scheme with several easy-to-implement computationaladvantages. The approach can be used with continuous and discrete,linear and nonlinear, mono-variable and multi-variable systems. Theestimators based on this approach are not of asymptotic nature, anddo not require any statistical knowledge of the corrupting noisesto achieve good performance in a noisy environment. Theseestimators are fast, robust to structured perturbations, and easyto combine with classical or sophisticated control laws. This book uses module theory, differential algebra, andoperational calculus in an easy-to-understand manner and alsodetails how to apply these in the context of feedback controlsystems. A wide variety of examples, including mechanical systems,power converters, electric motors, and chaotic systems, are alsoincluded to illustrate the algebraic methodology. Key features: Presents a radically new approach to online parameter and stateestimation. Enables the reader to master the use and understand theconsequences of the highly theoretical differential algebraicviewpoint in control systems theory. Includes examples in a variety of physical applications withexperimental results. Covers the latest developments and applications. Algebraic Identification and Estimation Methods in FeedbackControl Systems is a comprehensive reference for researchersand practitioners working in the area of automatic control, and isalso a useful source of information for graduate and undergraduatestudents.

## Directions in Mathematical Systems Theory and Optimization

**Author**: Anders Rantzer,Christopher I. Byrnes

**Publisher:**Springer Science & Business Media

**ISBN:**3540000658

**Category:**Computers

**Page:**391

**View:**1909

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For more than three decades, Anders Lindquist has delivered fundamental cont- butions to the ?elds of systems, signals and control. Throughout this period, four themes can perhaps characterize his interests: Modeling, estimation and ?ltering, feedback and robust control. His contributions to modeling include seminal work on the role of splitting subspaces in stochastic realization theory, on the partial realization problem for both deterministic and stochastic systems, on the solution of the rational covariance extension problem and on system identi?cation. His contributions to ?ltering and estimation include the development of fast ?ltering algorithms, leading to a nonlinear dynamical system which computes spectral factors in its steady state, and which provide an alternate, linear in the dimension of the state space, to computing the Kalman gain from a matrix Riccati equation. His further research on the phase portrait of this dynamical system gave a better understanding of when the Kalman ?lter will converge, answering an open question raised by Kalman. While still a student he established the separation principle for stochastic function differential equations, including some fundamental work on optimal control for stochastic systems with time lags. He continued his interest in feedback control by deriving optimal and robust control feedback laws for suppressing the effects of harmonic disturbances. Moreover, his recent work on a complete parameterization of all rational solutions to the Nevanlinna-Pick problem is providing a new approach to robust control design.

## Mathematical Methods for Robust and Nonlinear Control

*EPSRC Summer School*

**Author**: Matthew C. Turner,Declan G. Bates

**Publisher:**Springer Science & Business Media

**ISBN:**1848000251

**Category:**Technology & Engineering

**Page:**444

**View:**6600

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The underlying theory on which much modern robust and nonlinear control is based can be difficult to grasp. This volume is a collection of lecture notes presented by experts in advanced control engineering. The book is designed to provide a better grounding in the theory underlying several important areas of control. It is hoped the book will help the reader to apply otherwise abstruse ideas of nonlinear control in a variety of real systems.

## Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing

*10th International Conference, RSFDGrC 2005, Regina, Canada, August 31 - September 2, 2005, Proceedings*

**Author**: Dominik Ślęzak

**Publisher:**Springer Science & Business Media

**ISBN:**3540286608

**Category:**Artificial intelligence

**Page:**738

**View:**6488

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This volume contains the papers selected for presentation at the 10th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, RSFDGrC 2005, organized at the University of Regina, August 31st–September 3rd, 2005.

## Nonlinear System Identification

*From Classical Approaches to Neural Networks and Fuzzy Models*

**Author**: Oliver Nelles

**Publisher:**Springer Science & Business Media

**ISBN:**9783540673699

**Category:**Computers

**Page:**785

**View:**4344

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The goal of this book is to provide engineers and scientIsts in academia and industry with a thorough understanding of the underlying principles of nonlinear system identification. The reader will be able to apply the discussed models and methods to real problems with the necessary confidence and the awareness of potential difficulties that may arise in practice. This book is self-contained in the sense that it requires merely basic knowledge of matrix algebra, signals and systems, and statistics. Therefore, it also serves as an introduction to linear system identification and gives a practical overview on the major optimization methods used in engineering. The emphasis of this book is on an intuitive understanding of the subject and the practical application of the discussed techniques. It is not written in a theorem/proof style; rather the mathematics is kept to a minimum and the pursued ideas are illustrated by numerous figures, examples, and real-world applications. Fifteen years ago, nonlinear system identification was a field of several ad-hoc approaches, each applicable only to a very restricted class of systems. With the advent of neural networks, fuzzy models, and modern structure opti mization techniques a much wider class of systems can be handled. Although one major characteristic of nonlinear systems is that almost every nonlinear system is unique, tools have been developed that allow the use of the same ap proach for a broad variety of systems.