[PDF] Functional Analysis And Control Theory eBook

Author : S. Rolewicz
Publisher : Springer Science & Business Media
Page : 539 pages
File Size : 44,51 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 9401577587

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Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then, It is that they can't see the problem. one day, perhaps you will find the final G.K. Chesterton, The Scandal of Fa question. ther Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, cod ing theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

Author : J. R. Leigh
Publisher : Courier Corporation
Page : 178 pages
File Size : 18,10 MB
Release : 2007-03-16
Category : Technology & Engineering
ISBN : 048645813X

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Originally published: London; New York: Academic Press, 1980, in series: Mathematics in science and engineering; v. 156.

Author : Francis Clarke
Publisher : Springer Science & Business Media
Page : 589 pages
File Size : 13,92 MB
Release : 2013-02-06
Category : Mathematics
ISBN : 1447148207

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Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.

Author : Francis H. Clarke
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 43,98 MB
Release : 2008-01-10
Category : Mathematics
ISBN : 0387226257

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A clear and succinct presentation of the essentials of this subject, together with some of its applications and a generous helping of interesting exercises. Following an introductory chapter with a taste of what is to come, the next three chapters constitute a course in nonsmooth analysis and identify a coherent and comprehensive approach to the subject, leading to an efficient, natural, and powerful body of theory. The whole is rounded off with a self-contained introduction to the theory of control of ordinary differential equations. The authors have incorporated a number of new results which clarify the relationships between the different schools of thought in the subject, with the aim of making nonsmooth analysis accessible to a wider audience. End-of-chapter problems offer scope for deeper understanding.

Author : Amol Sasane
Publisher : Courier Corporation
Page : 154 pages
File Size : 41,28 MB
Release : 2013-04-10
Category : Mathematics
ISBN : 0486153312

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Accessible, undergraduate-level text illustrates the role of algebras of holomorphic functions in the stabilization of a linear control system. Concise, self-contained treatment avoids advanced mathematics. 2009 edition.

Author : Andrew J. Kurdila
Publisher : Springer Science & Business Media
Page : 238 pages
File Size : 35,49 MB
Release : 2006-03-30
Category : Science
ISBN : 3764373571

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This volume is dedicated to the fundamentals of convex functional analysis. It presents those aspects of functional analysis that are extensively used in various applications to mechanics and control theory. The purpose of the text is essentially two-fold. On the one hand, a bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis is presented. Numerous examples and diagrams provide as intuitive an explanation of the principles as possible. On the other hand, the volume is largely self-contained. Those with a background in graduate mathematics will find a concise summary of all main definitions and theorems.

Author : Anthony N. Michel
Publisher : Courier Corporation
Page : 514 pages
File Size : 20,4 MB
Release : 1993-01-01
Category : Mathematics
ISBN : 048667598X

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"A valuable reference." — American Scientist. Excellent graduate-level treatment of set theory, algebra and analysis for applications in engineering and science. Fundamentals, algebraic structures, vector spaces and linear transformations, metric spaces, normed spaces and inner product spaces, linear operators, more. A generous number of exercises have been integrated into the text. 1981 edition.