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Classical Control Using H-infinity Methods: Theory, Optimization, and Design

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by J. William Helton and Orlando Merino


1998 / xvi + 292 pages / Softcover / ISBN: 978-0-898714-19-7 / List Price $75.50 / SIAM Member Price $52.85 / Order Code OT65

"The books by Helton and Merino contain a wealth of material that can be used by students and researchers in a variety of different ways, depending on background and interests. To enhance this modular flexibility, the authors offer two versions ... Both versions contain introductory material, at an elementary level, on what control engineering is all about. ..." —Joseph A. Ball, SIAM Review, Volume 41, No. 4, December 1999.

"This book, treating control system design using H techniques and H theory motivated by control applications, is a very good tool for a large number of people interested in control and in H theory, from undergraduate students and engineers to research mathematicians. Here the reader can find answers to practical and theoretical problems, even by a partial reading, because the book is written in a highly modular way ..." —I. Valusescu, Zentralblatt für Mathematik, 1999.

" ... The authors make clear that a powerful and unified theory of H design is beginning to emerge, but that much remains to be done. The present book is a welcome contribution that should help to publicize the important advances that have been made and their potential for solving a difficult class of engineering control design problems." —N. Harris McClamroch, Mathematical Reviews, Issue 99i.

This versatile book teaches control system design using H techniques that are simple and compatible with classical control, yet powerful enough to quickly allow the solution of physically meaningful problems. The authors begin by teaching how to formulate control system design problems as mathematical optimization problems and then discuss the theory and numerics for these optimization problems. Their approach is simple and direct, and since the book is modular, the parts on theory can be read independently of the design parts and vice versa, allowing readers to enjoy the book on many levels.

The development of H engineering was one of the main accomplishments of control in the 1980s. However, until now, there has not been a publication suitable for teaching the topic at the undergraduate level. This book fills that gap by teaching control system design using H techniques at a level within reach of the typical engineering and mathematics student. It also contains a readable account of recent developments and mathematical connections.

The authors treat control design problems in a physically correct way. They present a small set of specific rules that the reader can apply to convert a particular design problem to the fundamental optimization problem of H control. This precisely formulated mathematics problem can then be solved on a computer. The book introduces the control software package OPTDesign, which allows the reader to easily reproduce the calculations done in the solved examples and even try variations on them. The description of how to convert an engineering problem to a form suitable for CAD is simpler than in other books.

This book is perfect as a supplementary text for both graduate and undergraduate engineering and mathematics students and is useful to working engineers because the methods are readily applicable in practical settings. Researchers in some branches of H control, amplifier design, and broadband antenna design will also have an interest in this book. Research mathematicians working in functional analysis, operator theory, and complex variables will find this volume a welcome addition to their library. Readers should be familiar with basic control concepts.

Recommended for an advanced seminar in control theory in engineering departments or applied functional analysis in mathematics departments, or for a second course in control at senior undergraduate or beginning graduate level.

Contents (abbreviated)
Preface; Part I: Short Design Course. Chapter 1: A Method for Solving System Design Problems; Chapter 2: Internal Stability; Chapter 3: Frequency Domain Performance Requirements; Chapter 4: Optimization; Review of Concepts; Chapter 5: A Design Example With OPTDesign; Part II: More on Design. Chapter 6: Examples; Chapter 7: Internal Stability; Part III: H Theory. Chapter 8: H Optimization and Control; Chapter 10: Facts About Analytic Functions; Chapter 11: Proof of the Main Result; Chapter 12: Computer Solutions to OPT; Part IV: H Theory: Vector Case. Chapter 13: Many Analytic Functions; Chapter 14: Coordinate Descent Approaches to OPT; Chapter 15: More Numerical Algorithms; Chapter 16: More Theory of the Vector OPT Problem; Part V: Semidefinite Programming vs. H Optimization. Chapter 17: Matrix H^\infty Optimization; Chapter 18: Numerical Algorithms for H Optimization; Chapter 19: Semidefinite Programming vs. Matrix H Optimization; Chapter 20: Proofs; Part VI: Appendices. Appendix A: History and Perspective; Appendix B: Pure Mathematics and H Optimization; Appendix C: Uncertainty; Appendix D: Computer Code for Examples in Chapter 6; Appendix E: Getting OPTDesign and Anopt; Appendix F: Anopt Notebook; Appendix G: NewtonInterpolant Notebook; Appendix H: NewtonFit Notebook.

ISBN: 9780898714197

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