Nonlinear Systems

Author: R. Sahadevan,Muthusamy Lakshmanan

Publisher: CRC Press

ISBN: 9780849317224

Category: Mathematics

Page: 384

View: 2062

Nonlinear Systems covers a wide range of topics in nonlinear science, from general nonlinear dynamics, soliton systems, and the solution of nonlinear differential and difference equations to the integrability of discrete nonlinear systems, and classical and quantum chaos. Its chapters reflect the current status of important nonlinear theories in various areas of applied mathematics and mathematical physics and collectively provide a comprehensive picture of new areas and their applications.

Nonlinear Systems

Author: Hassan K. Khalil

Publisher: N.A

ISBN: 9780130673893

Category: Mathematics

Page: 750

View: 1042

This book is written is such a way that the level of mathematical sophistication builds up from chapter to chapter. It has been reorganized into four parts: basic analysis, analysis of feedback systems, advanced analysis, and nonlinear feedback control. Updated content includes subjects which have proven useful in nonlinear control design in recent years—new in the 3rd edition are: expanded treatment of passivity and passivity-based control; integral control, high-gain feedback, recursive methods, optimal stabilizing control, control Lyapunov functions, and observers. For use as a self-study or reference guide by engineers and applied mathematicians.

Analysis and Control of Nonlinear Systems with Stationary Sets

Time-Domain and Frequency-Domain Methods

Author: Jinzhi Wang

Publisher: World Scientific

ISBN: 981281471X

Category: Electronic books

Page: 334

View: 5524

This book presents the analysis as well as methods based on the global properties of systems with stationary sets in a unified time-domain and frequency-domain framework. The focus is on multi-input and multi-output systems, compared to previous publications which considered only single-input and single-output systems. The control methods presented in this book will be valuable for research on nonlinear systems with stationary sets.

Active Disturbance Rejection Control for Nonlinear Systems

An Introduction

Author: Bao-Zhu Guo,Zhi-Liang Zhao

Publisher: John Wiley & Sons

ISBN: 1119239923

Category: Science

Page: 368

View: 8599

A concise, in-depth introduction to active disturbance rejection control theory for nonlinear systems, with numerical simulations and clearly worked out equations Provides the fundamental, theoretical foundation for applications of active disturbance rejection control Features numerical simulations and clearly worked out equations Highlights the advantages of active disturbance rejection control, including small overshooting, fast convergence, and energy savings

Computational Solution of Nonlinear Systems of Equations

Author: Eugene L. Allgower,Kurt Georg

Publisher: American Mathematical Soc.

ISBN: 9780821896945

Category: Mathematics

Page: 762

View: 7932

Nonlinear equations arise in essentially every branch of modern science, engineering, and mathematics. However, in only a very few special cases is it possible to obtain useful solutions to nonlinear equations via analytical calculations. As a result, many scientists resort to computational methods. This book contains the proceedings of the Joint AMS-SIAM Summer Seminar, ``Computational Solution of Nonlinear Systems of Equations,'' held in July 1988 at Colorado State University. The aim of the book is to give a wide-ranging survey of essentially all of the methods which comprise currently active areas of research in the computational solution of systems of nonlinear equations. A number of ``entry-level'' survey papers were solicited, and a series of test problems has been collected in an appendix. Most of the articles are accessible to students who have had a course in numerical analysis.

Nonlinear Systems Analysis

Second Edition

Author: M. Vidyasagar

Publisher: SIAM

ISBN: 0898715261

Category: Mathematics

Page: 498

View: 1645

This text provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations.

Nonlinear Systems

Analysis, Stability, and Control

Author: Shankar Sastry

Publisher: Springer Science & Business Media

ISBN: 1475731086

Category: Mathematics

Page: 668

View: 3344

There has been much excitement over the emergence of new mathematical techniques for the analysis and control of nonlinear systems. In addition, great technological advances have bolstered the impact of analytic advances and produced many new problems and applications which are nonlinear in an essential way. This book lays out in a concise mathematical framework the tools and methods of analysis which underlie this diversity of applications.

Nonlinear System Identification

From Classical Approaches to Neural Networks and Fuzzy Models

Author: Oliver Nelles

Publisher: Springer Science & Business Media

ISBN: 3662043238

Category: Technology & Engineering

Page: 786

View: 4738

Written from an engineering point of view, this book covers the most common and important approaches for the identification of nonlinear static and dynamic systems. The book also provides the reader with the necessary background on optimization techniques, making it fully self-contained. The new edition includes exercises.

Chaotic Dynamics of Nonlinear Systems

Author: S. Neil Rasband

Publisher: Courier Dover Publications

ISBN: 0486805778

Category: Science

Page: 240

View: 3933

Written when the young science of chaos was gaining a foothold in the scientific community, this book introduces the field's concepts, applications, theory, and technique. Suitable for advanced undergraduates and graduate students, researchers, and teachers of mathematics, physics, and engineering, the text's major prerequisite is familiarity with differential equations and linear vector spaces. Author S. Neil Rasband discusses the major models for the transitions to chaos exhibited by dynamic systems, introducing the "classical" topics and examples fundamental to the discipline. The most important routes to chaos are presented within a unified framework and supported by integrated problem sets. Topics include one- and two-dimensional maps, universality theory, fractal dimension, differential and conservative dynamics, and other subjects. The text is supplemented by a helpful glossary, references, and an index.

Toward Analytical Chaos in Nonlinear Systems

Author: Albert C. J. Luo

Publisher: John Wiley & Sons

ISBN: 1118887174

Category: Technology & Engineering

Page: 272

View: 7276

Exact analytical solutions to periodic motions in nonlineardynamical systems are almost not possible. Since the 18th century,one has extensively used techniques such as perturbation methods toobtain approximate analytical solutions of periodic motions innonlinear systems. However, the perturbation methods cannot providethe enough accuracy of analytical solutions of periodic motions innonlinear dynamical systems. So the bifurcation trees of periodicmotions to chaos cannot be achieved analytically. The authorhas developed an analytical technique that is more effective toachieve periodic motions and corresponding bifurcation trees tochaos analytically. Toward Analytical Chaos in Nonlinear Systemssystematically presents a new approach to analytically determineperiodic flows to chaos or quasi-periodic flows in nonlineardynamical systems with/without time-delay. It covers themathematical theory and includes two examples of nonlinear systemswith/without time-delay in engineering and physics. From theanalytical solutions, the routes from periodic motions to chaos aredeveloped analytically rather than the incomplete numerical routesto chaos. The analytical techniques presented will provide abetter understanding of regularity and complexity of periodicmotions and chaos in nonlinear dynamical systems. Key features: Presents the mathematical theory of analytical solutions ofperiodic flows to chaos or quasieriodic flows in nonlineardynamical systems Covers nonlinear dynamical systems and nonlinear vibrationsystems Presents accurate, analytical solutions of stable and unstableperiodic flows for popular nonlinear systems Includes two complete sample systems Discusses time-delayed, nonlinear systems and time-delayed,nonlinear vibrational systems Includes real world examples Toward Analytical Chaos in Nonlinear Systems is acomprehensive reference for researchers and practitioners acrossengineering, mathematics and physics disciplines, and is also auseful source of information for graduate and senior undergraduatestudents in these areas.

Nonlinear Systems

Stability and stabilization

Author: A.J. Fossard,D. Normand-Cyrot

Publisher: Springer Science & Business Media

ISBN: 9780412600005

Category: Technology & Engineering

Page: 244

View: 8141

Nonlinear Systems is divided into three volumes. The first deals with modeling and estimation, the second with stability and stabilization and the third with control. This three-volume set provides the most comprehensive and detailed reference available on nonlinear systems. Written by a group of leading experts in the field, drawn from industry, government and academic institutions, it provides a solid theoretical basis on nonlinear control methods as well as practical examples and advice for engineers, teachers and researchers working with nonlinear systems. Each book focuses on the applicability of the concepts introduced and keeps the level of mathematics to a minimum. Simulations and industrial examples drawn from aerospace as well as mechanical, electrical and chemical engineering are given throughout.

Nonlinear Systems

Author: P. G. Drazin

Publisher: Cambridge University Press

ISBN: 9780521406680

Category: Mathematics

Page: 317

View: 4383

A coherent treatment of nonlinear systems covering chaos, fractals, and bifurcation, as well as equilibrium, stability, and nonlinear oscillations. The systems treated are mostly of difference and differential equations. The author introduces the mathematical properties of nonlinear systems as an integrated theory, rather than simply presenting isolated fashionable topics. The topics are discussed in as concrete a way as possible, worked examples and problems are used to motivate and illustrate the general principles. More advanced parts of the text are denoted by asterisks, thus making it ideally suited to both undergraduate and graduate courses.

The Mechanics of Nonlinear Systems with Internal Resonances

Author: Arkadiy I. Manevich,Leonid Isaakovich Manevich

Publisher: Imperial College Press

ISBN: 9781860946820

Category: Science

Page: 276

View: 9566

One of the most important features of nonlinear systems with severaldegrees of freedom is the presence of internal resonances at certainrelations between natural frequencies of different modes. Thismonograph is the first book devoted predominantly to internalresonances in different mechanical systems including those ofpractical importance.

Nonlinear System Identification

NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains

Author: Stephen A. Billings

Publisher: John Wiley & Sons

ISBN: 1118535553

Category: Technology & Engineering

Page: 576

View: 9557

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.

Nonlinear Systems of Partial Differential Equations in Applied Mathematics

Author: Basil Nicolaenko,Darryl D. Holm,James M. Hyman,American Mathematical Society

Publisher: American Mathematical Soc.

ISBN: 9780821896907

Category: Mathematics

Page: 387

View: 7451

These two volumes of 47 papers focus on the increased interplay of theoretical advances in nonlinear hyperbolic systems, completely integrable systems, and evolutionary systems of nonlinear partial differential equations. The papers both survey recent results and indicate future research trends in these vital and rapidly developing branches of PDEs. The editor has grouped the papers loosely into the following five sections: integrable systems, hyperbolic systems, variational problems, evolutionary systems, and dispersive systems. However, the variety of the subjects discussed as well as their many interwoven trends demonstrate that it is through interactive advances that such rapid progress has occurred. These papers require a good background in partial differential equations. Many of the contributors are mathematical physicists, and the papers are addressed to mathematical physicists (particularly in perturbed integrable systems), as well as to PDE specialists and applied mathematicians in general.

Extending H-infinity Control to Nonlinear Systems

Control of Nonlinear Systems to Achieve Performance Objectives

Author: J. William Helton,Matthew R. James

Publisher: SIAM

ISBN: 0898714400

Category: Technology & Engineering

Page: 333

View: 9751

H-infinity control made considerable strides toward systematizing classical control. This bookaddresses how this extends to nonlinear systems.

Mathematical Methods for Scientists and Engineers

Linear and Nonlinear Systems

Author: Peter B. Kahn

Publisher: Courier Corporation

ISBN: 0486435164

Category: Mathematics

Page: 469

View: 7909

Appropriate for advanced undergraduate and graduate students in a variety of scientific and engineering fields, this text introduces linear and nonlinear problems and their associated models. The first part covers linear systems, emphasizing perturbation or approximation techniques and asymptotic methods. The second part comprises nonlinear problems, including weakly nonlinear oscillatory systems and nonlinear difference equations. The two parts, both of which include exercises, merge smoothly, and many of the nonlinear techniques arise from the study of the linear systems. 1990 edition. 70 figures. 4 tables. Appendix. Index.

Localization & Energy Transfer in Nonlinear Systems

Proceedings of the Third Conference : June 17-21 2002, San Lorenzo de El Escorial Madrid

Author: Robert Sinclair MacKay,Luis V zquez,Mar¡a Paz Zorzano

Publisher: World Scientific

ISBN: 9789812704627

Category: Mathematics

Page: 351

View: 6340

This conference was the third meeting organized in the framework of the European LOCNET project. The main topics discussed by this international research collaboration were localization by nonlinearity and spatial discreteness, and energy transfer (in crystals, biomolecules and Josephson arrays).

Intelligent Observer and Control Design for Nonlinear Systems

Author: Dierk Schröder

Publisher: Springer Science & Business Media

ISBN: 9783540636397

Category: Language Arts & Disciplines

Page: 339

View: 5734

Control theory of nonlinear systems, in which either the linear part is known but the relevant nonlinearities in place, kind or parameters are unknown, or both the linear and the nonlinear parts are partially or even most unknown, is a new, demanding and highly interesting field. This book treats the problem by focussing on the role of learning. Intelligent learning techniques are able to determine the unknown components of nonlinear systems. These processes are always stable and convergent. The methods presented can be used both on-line and off-line. They have applications in mechatronics, hydraulics and combustion engines.

Design Analysis

Mathematical Modeling of Nonlinear Systems

Author: David E. Thompson

Publisher: Cambridge University Press

ISBN: 9780521621700

Category: Mathematics

Page: 275

View: 8314

A 1999 text for graduate students and practising engineers, introducing mathematical modeling of engineering systems.