[PDF] Singular Perturbation Methods In Control eBook

Author : Petar Kokotovic
Publisher : SIAM
Page : 386 pages
File Size : 43,76 MB
Release : 1999-01-01
Category : Mathematics
ISBN : 9781611971118

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Singular perturbations and time-scale techniques were introduced to control engineering in the late 1960s and have since become common tools for the modeling, analysis, and design of control systems. In this SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications. This book continues to be essential in many ways. It lays down the foundation of singular perturbation theory for linear and nonlinear systems, it presents the methodology in a pedagogical way that is not available anywhere else, and it illustrates the theory with many solved examples, including various physical examples and applications. So while new developments may go beyond the topics covered in this book, they are still based on the methodology described here, which continues to be their common starting point.

Author : Desineni S. Naidu
Publisher : IET
Page : 314 pages
File Size : 50,75 MB
Release : 1988
Category : Technology & Engineering
ISBN : 9780863411076

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This book presents the twin topics of singular perturbation methods and time scale analysis to problems in systems and control. The heart of the book is the singularly perturbed optimal control systems, which are notorious for demanding excessive computational costs. The book addresses both continuous control systems (described by differential equations) and discrete control systems (characterised by difference equations).

Author : Robert E., Jr. O'Malley
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 43,9 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461209773

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This book results from various lectures given in recent years. Early drafts were used for several single semester courses on singular perturbation meth ods given at Rensselaer, and a more complete version was used for a one year course at the Technische Universitat Wien. Some portions have been used for short lecture series at Universidad Central de Venezuela, West Vir ginia University, the University of Southern California, the University of California at Davis, East China Normal University, the University of Texas at Arlington, Universita di Padova, and the University of New Hampshire, among other places. As a result, I've obtained lots of valuable feedback from students and listeners, for which I am grateful. This writing continues a pattern. Earlier lectures at Bell Laboratories, at the University of Edin burgh and New York University, and at the Australian National University led to my earlier works (1968, 1974, and 1978). All seem to have been useful for the study of singular perturbations, and I hope the same will be true of this monograph. I've personally learned much from reading and analyzing the works of others, so I would especially encourage readers to treat this book as an introduction to a diverse and exciting literature. The topic coverage selected is personal and reflects my current opin ions. An attempt has been made to encourage a consistent method of ap proaching problems, largely through correcting outer limits in regions of rapid change. Formal proofs of correctness are not emphasized.

Author : Ferdinand Verhulst
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 13,26 MB
Release : 2006-06-04
Category : Mathematics
ISBN : 0387283137

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Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach

Author : Lindsay A. Skinner
Publisher : Springer Science & Business Media
Page : 95 pages
File Size : 32,5 MB
Release : 2011-05-11
Category : Mathematics
ISBN : 1441999582

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This book is a rigorous presentation of the method of matched asymptotic expansions, the primary tool for attacking singular perturbation problems. A knowledge of conventional asymptotic analysis is assumed. The first chapter introduces the theory and is followed by four chapters of applications to ordinary differential equation problems of increasing complexity. Exercises are included as well as several Maple programs for computing the terms of the various asymptotic expansions that arise in solving the problems.

Author : E. J. Hinch
Publisher : Cambridge University Press
Page : 178 pages
File Size : 36,86 MB
Release : 1991-10-25
Category : Mathematics
ISBN : 9780521378970

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A textbook presenting the theory and underlying techniques of perturbation methods in a manner suitable for senior undergraduates from a broad range of disciplines.

Author : George G. Yin
Publisher : Springer
Page : 358 pages
File Size : 37,12 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461206278

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Using a singular perturbation approach, this is a systematic treatment of those systems that naturally arise in queuing theory, control and optimisation, and manufacturing, gathering a number of ideas which were previously scattered throughout the literature. The book presents results on asymptotic expansions of the corresponding probability distributions, functional occupation measures, exponential upper bounds, and asymptotic normality. To bridge the gap between theory and applications, a large portion of the book is devoted to various applications, thus reducing the dimensionality for problems under Markovian disturbances and providing tools for dealing with large-scale and complex real-world situations. Much of this stems from the authors'recent research, presenting results which have not appeared elsewhere. An important reference for researchers in applied mathematics, probability and stochastic processes, operations research, control theory, and optimisation.

Author : Alain Bensoussan
Publisher : Wiley
Page : 588 pages
File Size : 18,78 MB
Release : 1988-06-23
Category : Mathematics
ISBN : 9780471919940

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Describes, analyzes, and generalizes the principal results concerning perturbation methods in optimal control for systems governed by deterministic or stochastic differential equations. Covers the most important theorems in deterministic and stochastic optimal control, the theory of ergodic control, and the use of control, including regular perturbations and singular perturbations.

Author : Mark H. Holmes
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 15,1 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 1461253470

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This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.

Author : Robert E. Jr. O'Malley
Publisher : Elsevier
Page : 215 pages
File Size : 36,56 MB
Release : 2012-12-02
Category : Mathematics
ISBN : 0323162274

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Introduction to Singular Perturbations provides an overview of the fundamental techniques for obtaining asymptomatic solutions to boundary value problems. This text explores singular perturbation techniques, which are among the basic tools of several applied scientists. This book is organized into eight chapters, wherein Chapter 1 discusses the method of matched asymptomatic expansions, which has been frequently applied to several physical problems involving singular perturbations. Chapter 2 considers the nonlinear initial value problem to illustrate the regular perturbation method, and Chapter 3 explains how to construct asymptotic solutions for general linear equations. Chapter 4 discusses scalar equations and nonlinear system, whereas Chapters 5 and 6 explain the contrasts for initial value problems where the outer expansion cannot be determined without obtaining the initial values of the boundary layer correction. Chapters 7 and 8 deal with boundary value problem that arises in the study of adiabatic tubular chemical flow reactors with axial diffusion. This monograph is a valuable resource for applied mathematicians, engineers, researchers, students, and readers whose interests span a variety of fields.