Nonlinear Systems, Vol. 2

Nonlinear Systems, Vol. 2
Author: Juan F. R. Archilla
Publisher: Springer
Total Pages: 350
Release: 2017-12-21
Genre: Science
ISBN: 3319722182

This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction arrays, waveguide arrays, photonic crystals and optical fibers. Nonlinear excitations are inherent to Bose-Einstein Condensates, constituting an excellent benchmark for testing their properties and providing a pathway for future discoveries in fundamental physics.

Nonlinear Systems

Nonlinear Systems
Author: P. G. Drazin
Publisher: Cambridge University Press
Total Pages: 354
Release: 1992-06-26
Genre: Mathematics
ISBN: 9780521406680

The theories of bifurcation, chaos and fractals as well as equilibrium, stability and nonlinear oscillations, are part of the theory of the evolution of solutions of nonlinear equations. A wide range of mathematical tools and ideas are drawn together in the study of these solutions, and the results applied to diverse and countless problems in the natural and social sciences, even philosophy. The text evolves from courses given by the author in the UK and the United States. It introduces the mathematical properties of nonlinear systems, mostly difference and differential equations, as an integrated theory, rather than presenting isolated fashionable topics. Topics are discussed in as concrete a way as possible and worked examples and problems are used to explain, motivate and illustrate the general principles. The essence of these principles, rather than proof or rigour, is emphasized. More advanced parts of the text are denoted by asterisks, and the mathematical prerequisites are limited to knowledge of linear algebra and advanced calculus, thus making it ideally suited to both senior undergraduates and postgraduates from physics, engineering, chemistry, meteorology etc. as well as mathematics.

Stability and Stabilization of Nonlinear Systems

Stability and Stabilization of Nonlinear Systems
Author: Iasson Karafyllis
Publisher: Springer Science & Business Media
Total Pages: 401
Release: 2011-04-02
Genre: Technology & Engineering
ISBN: 0857295136

Recently, the subject of nonlinear control systems analysis has grown rapidly and this book provides a simple and self-contained presentation of their stability and feedback stabilization which enables the reader to learn and understand major techniques used in mathematical control theory. In particular: the important techniques of proving global stability properties are presented closely linked with corresponding methods of nonlinear feedback stabilization; a general framework of methods for proving stability is given, thus allowing the study of a wide class of nonlinear systems, including finite-dimensional systems described by ordinary differential equations, discrete-time systems, systems with delays and sampled-data systems; approaches to the proof of classical global stability properties are extended to non-classical global stability properties such as non-uniform-in-time stability and input-to-output stability; and new tools for stability analysis and control design of a wide class of nonlinear systems are introduced. The presentational emphasis of Stability and Stabilization of Nonlinear Systems is theoretical but the theory’s importance for concrete control problems is highlighted with a chapter specifically dedicated to applications and with numerous illustrative examples. Researchers working on nonlinear control theory will find this monograph of interest while graduate students of systems and control can also gain much insight and assistance from the methods and proofs detailed in this book.

Nonlinear Control Systems

Nonlinear Control Systems
Author: Alberto Isidori
Publisher: Springer Science & Business Media
Total Pages: 557
Release: 2013-04-17
Genre: Technology & Engineering
ISBN: 1846286158

The purpose of this book is to present a self-contained description of the fun damentals of the theory of nonlinear control systems, with special emphasis on the differential geometric approach. The book is intended as a graduate text as weil as a reference to scientists and engineers involved in the analysis and design of feedback systems. The first version of this book was written in 1983, while I was teach ing at the Department of Systems Science and Mathematics at Washington University in St. Louis. This new edition integrates my subsequent teaching experience gained at the University of Illinois in Urbana-Champaign in 1987, at the Carl-Cranz Gesellschaft in Oberpfaffenhofen in 1987, at the University of California in Berkeley in 1988. In addition to a major rearrangement of the last two Chapters of the first version, this new edition incorporates two additional Chapters at a more elementary level and an exposition of some relevant research findings which have occurred since 1985.

Analysis and Control of Nonlinear Systems

Analysis and Control of Nonlinear Systems
Author: Jean Levine
Publisher: Springer Science & Business Media
Total Pages: 322
Release: 2009-05-28
Genre: Technology & Engineering
ISBN: 3642008399

This book examines control of nonlinear systems. Coverage ranges from mathematical system theory to practical industrial control applications. The author offers web-based videos illustrating some dynamical aspects and case studies in simulation.

Introduction to Applied Nonlinear Dynamical Systems and Chaos

Introduction to Applied Nonlinear Dynamical Systems and Chaos
Author: Stephen Wiggins
Publisher: Springer Science & Business Media
Total Pages: 860
Release: 2006-04-18
Genre: Mathematics
ISBN: 0387217495

This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms. From the reviews: "Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik

Structural Sensitivity Analysis and Optimization 2

Structural Sensitivity Analysis and Optimization 2
Author: K. K. Choi
Publisher: Springer Science & Business Media
Total Pages: 336
Release: 2006-12-22
Genre: Science
ISBN: 0387273069

Extensive numerical methods for computing design sensitivity are included in the text for practical application and software development. The numerical method allows integration of CAD-FEA-DSA software tools, so that design optimization can be carried out using CAD geometric models instead of FEA models. This capability allows integration of CAD-CAE-CAM so that optimized designs can be manufactured effectively.

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
Author: John Guckenheimer
Publisher: Springer Science & Business Media
Total Pages: 475
Release: 2013-11-21
Genre: Mathematics
ISBN: 1461211409

An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

Linear, Time-varying Approximations to Nonlinear Dynamical Systems

Linear, Time-varying Approximations to Nonlinear Dynamical Systems
Author: Maria Tomas-Rodriguez
Publisher: Springer Science & Business Media
Total Pages: 303
Release: 2010-02-04
Genre: Mathematics
ISBN: 184996100X

Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those – well-known – based on differential geometry. The authors cover many aspects of nonlinear systems including stability theory, control design and extensions to distributed parameter systems. Many of the classical and modern control design methods which can be applied to linear, time-varying systems can be extended to nonlinear systems by this technique. The implementation of the control is therefore simple and can be done with well-established classical methods. Many aspects of nonlinear systems, such as spectral theory which is important for the generalisation of frequency domain methods, can be approached by this method.

Stable Adaptive Control and Estimation for Nonlinear Systems

Stable Adaptive Control and Estimation for Nonlinear Systems
Author: Jeffrey T. Spooner
Publisher: John Wiley & Sons
Total Pages: 564
Release: 2004-04-07
Genre: Science
ISBN: 0471460974

Thema dieses Buches ist die Anwendung neuronaler Netze und Fuzzy-Logic-Methoden zur Identifikation und Steuerung nichtlinear-dynamischer Systeme. Dabei werden fortgeschrittene Konzepte der herkömmlichen Steuerungstheorie mit den intuitiven Eigenschaften intelligenter Systeme kombiniert, um praxisrelevante Steuerungsaufgaben zu lösen. Die Autoren bieten viel Hintergrundmaterial; ausgearbeitete Beispiele und Übungsaufgaben helfen Studenten und Praktikern beim Vertiefen des Stoffes. Lösungen zu den Aufgaben sowie MATLAB-Codebeispiele sind ebenfalls enthalten.