Nonlinear Dynamical Systems And Carleman Linearization
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Nonlinear Dynamical Systems And Carleman Linearization
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Author : Krzysztof Kowalski
language : en
Publisher: World Scientific
Release Date : 1991-03-26
Nonlinear Dynamical Systems And Carleman Linearization written by Krzysztof Kowalski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-03-26 with Mathematics categories.
The Carleman linearization has become a new powerful tool in the study of nonlinear dynamical systems. Nevertheless, there is the general lack of familiarity with the Carleman embedding technique among those working in the field of nonlinear models. This book provides a systematic presentation of the Carleman linearization, its generalizations and applications. It also includes a review of existing alternative methods for linearization of nonlinear dynamical systems. There are probably no books covering such a wide spectrum of linearization algorithms. This book also gives a comprehensive introduction to the Kronecker product of matrices, whereas most books deal with it only superficially. The Kronecker product of matrices plays an important role in mathematics and in applications found in theoretical physics.
Methods Of Hilbert Spaces In The Theory Of Nonlinear Dynamical Systems
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Author : Krzysztof Kowalski
language : en
Publisher: World Scientific
Release Date : 1994
Methods Of Hilbert Spaces In The Theory Of Nonlinear Dynamical Systems written by Krzysztof Kowalski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This book is the first monograph on a new powerful method discovered by the author for the study of nonlinear dynamical systems relying on reduction of nonlinear differential equations to the linear abstract Schrdinger-like equation in Hilbert space. Besides the possibility of unification of many apparently completely different techniques, the ?quantal? Hilbert space formalism introduced enables new original methods to be discovered for solving nonlinear problems arising in investigation of ordinary and partial differential equations as well as difference equations. Applications covered in the book include symmetries and first integrals, linearization transformations, Bcklund transformations, stroboscopic maps, functional equations involving the case of Feigenbaum-Cvitanovic renormalization equations and chaos.
Nonlinear Dynamical Systems Of Mathematical Physics
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Author : Denis L. Blackmore
language : en
Publisher: World Scientific
Release Date : 2011
Nonlinear Dynamical Systems Of Mathematical Physics written by Denis L. Blackmore and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field - including some innovations by the authors themselves - that have not appeared in any other book. The exposition begins with an introduction to modern integrable dynamical systems theory, treating such topics as Liouville?Arnold and Mischenko?Fomenko integrability. This sets the stage for such topics as new formulations of the gradient-holonomic algorithm for Lax integrability, novel treatments of classical integration by quadratures, Lie-algebraic characterizations of integrability, and recent results on tensor Poisson structures. Of particular note is the development via spectral reduction of a generalized de Rham?Hodge theory, related to Delsarte-Lions operators, leading to new Chern type classes useful for integrability analysis. Also included are elements of quantum mathematics along with applications to Whitham systems, gauge theories, hadronic string models, and a supplement on fundamental differential-geometric concepts making this volume essentially self-contained. This book is ideal as a reference and guide to new directions in research for advanced students and researchers interested in the modern theory and applications of integrable (especially infinite-dimensional) dynamical systems.
Linearization Methods For Stochastic Dynamic Systems
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Author : Leslaw Socha
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-20
Linearization Methods For Stochastic Dynamic Systems written by Leslaw Socha and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-20 with Technology & Engineering categories.
For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. This book details the relatively simple and popular linearization techniques available, covering theory as well as application. It examines models with continuous external and parametric excitations, those that cover the majority of known approaches.
Applications Of Nonlinear Dynamics
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Author : Visarath In
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-11
Applications Of Nonlinear Dynamics written by Visarath In and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-11 with Technology & Engineering categories.
The ?eld of applied nonlinear dynamics has attracted scientists and engineers across many different disciplines to develop innovative ideas and methods to study c- plex behavior exhibited by relatively simple systems. Examples include: population dynamics, ?uidization processes, applied optics, stochastic resonance, ?ocking and ?ightformations,lasers,andmechanicalandelectricaloscillators. Acommontheme among these and many other examples is the underlying universal laws of nonl- ear science that govern the behavior, in space and time, of a given system. These laws are universal in the sense that they transcend the model-speci?c features of a system and so they can be readily applied to explain and predict the behavior of a wide ranging phenomena, natural and arti?cial ones. Thus the emphasis in the past decades has been in explaining nonlinear phenomena with signi?cantly less att- tion paid to exploiting the rich behavior of nonlinear systems to design and fabricate new devices that can operate more ef?ciently. Recently, there has been a series of meetings on topics such as Experimental Chaos, Neural Coding, and Stochastic Resonance, which have brought together many researchers in the ?eld of nonlinear dynamics to discuss, mainly, theoretical ideas that may have the potential for further implementation. In contrast, the goal of the 2007 ICAND (International Conference on Applied Nonlinear Dynamics) was focused more sharply on the implementation of theoretical ideas into actual - vices and systems.
Nonlinear Control Systems 2004
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Author : Frank Allgower
language : en
Publisher: Elsevier
Release Date : 2005-02-02
Nonlinear Control Systems 2004 written by Frank Allgower and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-02 with Science categories.
The Koopman Operator In Systems And Control
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Author : Alexandre Mauroy
language : en
Publisher: Springer Nature
Release Date : 2020-02-22
The Koopman Operator In Systems And Control written by Alexandre Mauroy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-22 with Technology & Engineering categories.
This book provides a broad overview of state-of-the-art research at the intersection of the Koopman operator theory and control theory. It also reviews novel theoretical results obtained and efficient numerical methods developed within the framework of Koopman operator theory. The contributions discuss the latest findings and techniques in several areas of control theory, including model predictive control, optimal control, observer design, systems identification and structural analysis of controlled systems, addressing both theoretical and numerical aspects and presenting open research directions, as well as detailed numerical schemes and data-driven methods. Each contribution addresses a specific problem. After a brief introduction of the Koopman operator framework, including basic notions and definitions, the book explores numerical methods, such as the dynamic mode decomposition (DMD) algorithm and Arnoldi-based methods, which are used to represent the operator in a finite-dimensional basis and to compute its spectral properties from data. The main body of the book is divided into three parts: theoretical results and numerical techniques for observer design, synthesis analysis, stability analysis, parameter estimation, and identification; data-driven techniques based on DMD, which extract the spectral properties of the Koopman operator from data for the structural analysis of controlled systems; and Koopman operator techniques with specific applications in systems and control, which range from heat transfer analysis to robot control. A useful reference resource on the Koopman operator theory for control theorists and practitioners, the book is also of interest to graduate students, researchers, and engineers looking for an introduction to a novel and comprehensive approach to systems and control, from pure theory to data-driven methods.
Mathematical Control Theory And Finance
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Author : Andrey Sarychev
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-31
Mathematical Control Theory And Finance written by Andrey Sarychev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-31 with Mathematics categories.
Control theory provides a large set of theoretical and computational tools with applications in a wide range of ?elds, running from ”pure” branches of mathematics, like geometry, to more applied areas where the objective is to ?nd solutions to ”real life” problems, as is the case in robotics, control of industrial processes or ?nance. The ”high tech” character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the ?nancial analyst to possess a high level of mathematical skills. C- versely, the complex challenges posed by the problems and models relevant to ?nance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from stochastic optimal control constitutes a well established and important branch of mathematical ?nance. Up to now, other branches of control theory have found comparatively less application in ?n- cial problems. To some extent, deterministic and stochastic control theories developed as di?erent branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these ?elds has intensi?ed. Some concepts from stochastic calculus (e.g., rough paths) havedrawntheattentionofthedeterministiccontroltheorycommunity.Also, some ideas and tools usual in deterministic control (e.g., geometric, algebraic or functional-analytic methods) can be successfully applied to stochastic c- trol.
Nonlinear Workbook The Chaos Fractals Cellular Automata Neural Networks Genetic Algorithms Fuzzy Logic With C Java Symbolicc And Reduce Programs
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Author : Willi-hans Steeb
language : en
Publisher: World Scientific Publishing Company
Release Date : 1999-08-17
Nonlinear Workbook The Chaos Fractals Cellular Automata Neural Networks Genetic Algorithms Fuzzy Logic With C Java Symbolicc And Reduce Programs written by Willi-hans Steeb and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-08-17 with Nonlinear programming categories.
This book provides all the techniques and methods used in nonlinear dynamics. All the concepts are discussed in detail. The numerical and symbolic methods are implemented using C++, Java, SymbolicC++ and Reduce.
Nonlinear Workbook The Chaos Fractals Cellular Automata Neural Networks Genetic Algorithms Gene Expression Programming Wavelets Fuzzy Logic With C Java And Symbolic C Programs 2nd Edition
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Author : Willi-hans Steeb
language : en
Publisher: World Scientific Publishing Company
Release Date : 2002-12-30
Nonlinear Workbook The Chaos Fractals Cellular Automata Neural Networks Genetic Algorithms Gene Expression Programming Wavelets Fuzzy Logic With C Java And Symbolic C Programs 2nd Edition written by Willi-hans Steeb and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-30 with categories.
New Edition: The Nonlinear Workbook (6th Edition)The study of nonlinear dynamical systems has advanced tremendously in the last 15 years, making a big impact on science and technology. This book provides all the techniques and methods used in nonlinear dynamics. The concepts and underlying mathematics are discussed in detail.The numerical and symbolic methods are implemented in C++, SymbolicC++ and Java. Object-oriented techniques are also applied. The book contains more than 100 ready-to-run programs.The text has also been designed for a one-year course at both the junior and senior levels in nonlinear dynamics. The topics discussed in the book are part of e-learning and distance learning courses conducted by the International School for Scientific Computing.