Averaging in Stability Theory

.'; 'One service logic has rendered com­ puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And alI statements obtainable this way form part of the raison d'etre of this series.

Author: M.M. Hapaev

Publisher: Springer

ISBN: 9401051682

Category: Mathematics

Page: 279

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One service mathematics has rmdcred the 'Et moi, .•.• si j'avait su comment en rcvenir. human race. It has put common sense back je n'y semis point aile.' whc:rc it belongs, on the topmost shcIl next Jules Verne to the dusty callister labc:1lcd 'discarded non­ sense'. The series is divergent; thererore we may be Eric T. Bell able to do something with iL O. Hcavisidc Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com­ puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And alI statements obtainable this way form part of the raison d'etre of this series.
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Method of Averaging for Differential Equations on an Infinite Interval

Encompassing these novel aspects, Method of Averaging of the Infinite Interval: Theory and Applications rigorously explains the modern theory of the method of averaging and provides a solid understanding of the results obtained when ...

Author: Vladimir Burd

Publisher: Chapman and Hall/CRC

ISBN: UVA:X030260537

Category: Mathematics

Page: 343

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Explains the modern theory of the method of averaging and provides a understanding of the results obtained when applying this theory. This book starts with the less complicated theory of averaging linear differential equations (LDEs), focusing on almost periodic functions. It also includes chapters devoted to systems with a rapidly rotating phase.
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Stability Analysis

Filatov , A. N. [ 1 ] Averaging Methods for Differential and Integro - Differential Equations . ... [ Russian ] Gradstein , W. S. [ 1 ] The application of Lyapunov stability theory to the theory of differential equations with small ...

Author: Martynuk

Publisher: CRC Press

ISBN: 288449023X

Category: Science

Page: 336

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Advanced Tokamak Stability Theory

The gyrophase-average of the second term on the right-hand side of (4.54) yields iωdξ in (A.12) · ∇Fg and 0. One therefore can prove should that be this kept. term is of order ω*/ω compared to the first term The gyrophase-average of ...

Author: Linjin Zheng

Publisher: Morgan & Claypool Publishers

ISBN: 9781627054232

Category: Science

Page: 165

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This book describes the advanced stability theories for magnetically confined fusion plasmas, especially in tokamaks. As the fusion plasma sciences advance, the gap between the textbooks and cutting-edge researches gradually develops. This book fills in
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Stochastic Averaging and Stochastic Extremum Seeking

... algorithms and stability theory. Unfortunately, existing stochastic averaging theorems in continuous time are too restrictive to be applicable to extremum seeking algorithms. Such algorithms violate the global Lipschitz assumptions, ...

Author: Shu-Jun Liu

Publisher: Springer Science & Business Media

ISBN: 9781447140870

Category: Technology & Engineering

Page: 224

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Stochastic Averaging and Extremum Seeking treats methods inspired by attempts to understand the seemingly non-mathematical question of bacterial chemotaxis and their application in other environments. The text presents significant generalizations on existing stochastic averaging theory developed from scratch and necessitated by the need to avoid violation of previous theoretical assumptions by algorithms which are otherwise effective in treating these systems. Coverage is given to four main topics. Stochastic averaging theorems are developed for the analysis of continuous-time nonlinear systems with random forcing, removing prior restrictions on nonlinearity growth and on the finiteness of the time interval. The new stochastic averaging theorems are usable not only as approximation tools but also for providing stability guarantees. Stochastic extremum-seeking algorithms are introduced for optimization of systems without available models. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms for non-cooperative/adversarial games is described. The analysis of their convergence to Nash equilibria is provided. The algorithms are illustrated on models of economic competition and on problems of the deployment of teams of robotic vehicles. Bacterial locomotion, such as chemotaxis in E. coli, is explored with the aim of identifying two simple feedback laws for climbing nutrient gradients. Stochastic extremum seeking is shown to be a biologically-plausible interpretation for chemotaxis. For the same chemotaxis-inspired stochastic feedback laws, the book also provides a detailed analysis of convergence for models of nonholonomic robotic vehicles operating in GPS-denied environments. The book contains block diagrams and several simulation examples, including examples arising from bacterial locomotion, multi-agent robotic systems, and economic market models. Stochastic Averaging and Extremum Seeking will be informative for control engineers from backgrounds in electrical, mechanical, chemical and aerospace engineering and to applied mathematicians. Economics researchers, biologists, biophysicists and roboticists will find the applications examples instructive.
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Method of Averaging for Differential Equations on an Infinite Interval

Theory and Applications Vladimir Burd. and stability of periodic and almost periodic solutions. In the third chapter the method of averaging is applied to the study of the stability of equilibriums of various pendulum systems with an ...

Author: Vladimir Burd

Publisher: CRC Press

ISBN: 158488875X

Category: Mathematics

Page: 360

View: 936

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In recent years, mathematicians have detailed simpler proofs of known theorems, have identified new applications of the method of averaging, and have obtained many new results of these applications. Encompassing these novel aspects, Method of Averaging of the Infinite Interval: Theory and Applications rigorously explains the modern theory of the method of averaging and provides a solid understanding of the results obtained when applying this theory. The book starts with the less complicated theory of averaging linear differential equations (LDEs), focusing on almost periodic functions. It describes stability theory and Shtokalo's method, and examines various applications, including parametric resonance and the construction of asymptotics. After establishing this foundation, the author goes on to explore nonlinear equations. He studies standard form systems in which the right-hand side of a system is proportional to a small parameter and proves theorems similar to Banfi's theorem. The final chapters are devoted to systems with a rapidly rotating phase. Covering an important asymptotic method of differential equations, this book provides a thorough understanding of the method of averaging theory and its resulting applications.
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Pulsewidth Modulated DC to DC Power Conversion

It the averaging operation discussed in Section 5.2 is executed on the stable periodic waveforms, the resulting ... Accordingly, we could adapt the stability theory to the average model of a dc-to-dc converter to test whether the ...

Author: Byungcho Choi

Publisher: John Wiley & Sons

ISBN: 9781118753576

Category: Technology & Engineering

Page: 664

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This is the definitive reference for anyone involved in pulsewidth modulated DC-to-DC power conversion Pulsewidth Modulated DC-to-DC Power Conversion: Circuits, Dynamics, and Control Designs provides engineers, researchers, and students in the power electronics field with comprehensive and complete guidance to understanding pulsewidth modulated (PWM) DC-to-DC power converters. Presented in three parts, the book addresses the circuitry and operation of PWM DC-to-DC converters and their dynamic characteristics, along with in-depth discussions of control design of PWM DC-to-DC converters. Topics include: Basics of DC-to-DC power conversion DC-to-DC converter circuits Dynamic modeling Power stage dynamics Closed-loop performance Voltage mode control and feedback design Current mode control and compensation design Sampling effects of current mode control Featuring fully tested problems and simulation examples as well as downloadable lecture slides and ready-to-run PSpice programs, Pulsewidth Modulated DC-to-DC Power Conversion is an ideal reference book for professional engineers as well as graduate and undergraduate students.
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Advances in Learning Theory

In next section , we show as an aside a way of improving the stability of a learning algorithm by averaging techniques . 6.3.4 Stability of averaging techniques Suppose that a learning algorithm A has uniform stability Bm = 0 ( 1 / mo ) ...

Author: Johan A. K. Suykens

Publisher: IOS Press

ISBN: 1586033417

Category: Computational learning theory

Page: 415

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This text details advances in learning theory that relate to problems studied in neural networks, machine learning, mathematics and statistics.
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Reflection and the Stability of Belief

An average stability theory takes its cue from the fact that periods of intense reflection are brief; it assesses stability in terms of the (weighted) average stability of beliefs over time. A subject's faculties can tend to a high ...

Author: Louis E. Loeb

Publisher: Oxford University Press

ISBN: 9780199709311

Category: Philosophy

Page:

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A unifying theme of Loeb's work is epistemological - that Descartes and Hume advance theories of knowledge that rely on a substantial 'naturalistic' component, adopting one or another member of a cluster of psychological properties of beliefs as the goal of inquiry and the standard for assessing belief-forming mechanisms. Thus Loeb shows a surprising affinity between the epistemologies of the two figures -- surprising because they are often thought of as polar opposites in this respect. Descartes and Hume are unique in that their philosophical texts are accessible beyond just a narrow audience in the history of philosophy; their ideas continue to be a vital part of the field at large. This volume will thus appeal to advanced students and scholars not just in the history of early modern philosophy but in epistemology and other core areas of the discipline.
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The Stability Theory of Stream Ciphers

We call a fixed - length source code C of length n conditionally stable if Pc satisfies 1 = min { [ PD D is a source code for U with 2 codeword length n } Similarly , a variable - length code with average length n is said to be ...

Author: Cunsheng Ding

Publisher: Springer Science & Business Media

ISBN: 3540549730

Category: Computers

Page: 187

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Secure message transmission is of extreme importance in today's information-based society. Stream encryption is a practically important means to this end. This monograph is devoted to a new aspect of stream ciphers, namely the stability theory of stream ciphers, with the purpose of developing bounds on complexity which can form part of the basis for a general theory of data security and of stabilizing stream-cipher systems. The approach adopted in this monograph is new. The topic is treated by introducing measure indexes on the security of stream ciphers, developing lower bounds on these indexes, and establishing connections among them. The treatment involves the stability of boolean functions, the stability of linear complexity of key streams, the period stability of key streams, and the stability of source codes. Misleading ideas about stream ciphers are exposed and new viewpoints presented. The numerous measure indexes and bounds on them that are introduced here, the approach based on spectrum techniques, andthe ten open problems presented will all be useful to the reader concerned with analyzing and designing stream ciphers for securing data.
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