Algebraic And Geometric Methods In Nonlinear Control Theory
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Algebraic And Geometric Methods In Nonlinear Control Theory
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Author : M. Fliess
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic And Geometric Methods In Nonlinear Control Theory written by M. Fliess 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 2012-12-06 with Mathematics categories.
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point"of a Pin'. van GuIik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs 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; ihe Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras ·are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Algebraic And Geometric Methods In Nonlinear Control Theory
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Author : M Fliess
language : en
Publisher:
Release Date : 1986-07-31
Algebraic And Geometric Methods In Nonlinear Control Theory written by M Fliess and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-07-31 with categories.
Algebraic Methods For Nonlinear Control Systems
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Author : Giuseppe Conte
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-19
Algebraic Methods For Nonlinear Control Systems written by Giuseppe Conte 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 2007-01-19 with Technology & Engineering categories.
A self-contained introduction to algebraic control for nonlinear systems suitable for researchers and graduate students. "Algebraic Methods for Nonlinear Control Systems" develops a linear-algebraic alternative to the usual differential-geometric approach to nonlinear control, using vector spaces over suitable fields of nonlinear functions. It describes a range of results, some of which can be derived using differential geometry but many of which cannot. They include: classical and generalized realization in the nonlinear context; accessibility and observability recast for the linear-algebraic setting; discussion and solution of basic feedback problems; results for dynamic and static state and output feedback. Dynamic feedback and realization are shown to be dealt with and solved much more easily in the algebraic framework. The second edition has been completely revised with new text, examples and exercises; it is divided into two parts: necessary methodology and applications to control problems.
Control Theory From The Geometric Viewpoint
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Author : Andrei A. Agrachev
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-04-15
Control Theory From The Geometric Viewpoint written by Andrei A. Agrachev 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 2004-04-15 with Language Arts & Disciplines categories.
This book presents some facts and methods of Mathematical Control Theory treated from the geometric viewpoint. It is devoted to finite-dimensional deterministic control systems governed by smooth ordinary differential equations. The problems of controllability, state and feedback equivalence, and optimal control are studied. Some of the topics treated by the authors are covered in monographic or textbook literature for the first time while others are presented in a more general and flexible setting than elsewhere. Although being fundamentally written for mathematicians, the authors make an attempt to reach both the practitioner and the theoretician by blending the theory with applications. They maintain a good balance between the mathematical integrity of the text and the conceptual simplicity that might be required by engineers. It can be used as a text for graduate courses and will become most valuable as a reference work for graduate students and researchers.
Nonlinear Systems Analysis
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Author : M. Vidyasagar
language : en
Publisher: SIAM
Release Date : 2002-01-01
Nonlinear Systems Analysis written by M. Vidyasagar and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques because virtually all physical systems are nonlinear in nature. The second edition, now republished in SIAM's Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. Audience: this text is designed for use at the graduate level in the area of nonlinear systems and as a resource for professional researchers and practitioners working in areas such as robotics, spacecraft control, motor control, and power systems.
Geometric Control Theory
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Author : Velimir Jurdjevic
language : en
Publisher: Cambridge University Press
Release Date : 1997
Geometric Control Theory written by Velimir Jurdjevic and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Geometric control theory is concerned with the evolution of systems subject to physical laws but having some degree of freedom through which motion is to be controlled. This book describes the mathematical theory inspired by the irreversible nature of time evolving events. The first part of the book deals with the issue of being able to steer the system from any point of departure to any desired destination. The second part deals with optimal control, the question of finding the best possible course. An overlap with mathematical physics is demonstrated by the Maximum principle, a fundamental principle of optimality arising from geometric control, which is applied to time-evolving systems governed by physics as well as to man-made systems governed by controls. Applications are drawn from geometry, mechanics, and control of dynamical systems. The geometric language in which the results are expressed allows clear visual interpretations and makes the book accessible to physicists and engineers as well as to mathematicians.
Geometric Control Of Mechanical Systems
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Author : Francesco Bullo
language : en
Publisher: Springer
Release Date : 2019-06-12
Geometric Control Of Mechanical Systems written by Francesco Bullo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-12 with Science categories.
The primary emphasis of this book is the modeling, analysis, and control of mechanical systems. The methods and results presented can be applied to a large class of mechanical control systems, including applications in robotics, autonomous vehicle control, and multi-body systems. The book is unique in that it presents a unified, rather than an inclusive, treatment of control theory for mechanical systems. A distinctive feature of the presentation is its reliance on techniques from differential and Riemannian geometry. The book contains extensive examples and exercises, and will be suitable for a growing number of courses in this area. It begins with the detailed mathematical background, proceeding through innovative approaches to physical modeling, analysis, and design techniques. Numerous examples illustrate the proposed methods and results, while the many exercises test basic knowledge and introduce topics not covered in the main body of the text. The audience of this book consists of two groups. The first group is comprised of graduate students in engineering or mathematical sciences who wish to learn the basics of geometric mechanics, nonlinear control theory, and control theory for mechanical systems. Readers will be able to immediately begin exploring the research literature on these subjects. The second group consists of researchers in mechanics and control theory. Nonlinear control theoreticians will find explicit links between concepts in geometric mechanics and nonlinear control theory. Researchers in mechanics will find an overview of topics in control theory that have relevance to mechanics.
Conference On The Algebraic And Geometric Methods In Non Linear Control Theory
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Author : Société de mathématiques appliquées et industrielles (France).
language : en
Publisher:
Release Date : 1985
Conference On The Algebraic And Geometric Methods In Non Linear Control Theory written by Société de mathématiques appliquées et industrielles (France). and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
Nonlinear Control Systems
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Author : Alberto Isidori
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Nonlinear Control Systems written by Alberto Isidori 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 2013-04-17 with Technology & Engineering categories.
The purpose of this book is to present a self-contained description of the fun damentals of the theory of nonlinear control systems, with special emphasis on the differential geometric approach. The book is intended as a graduate text as weil as a reference to scientists and engineers involved in the analysis and design of feedback systems. The first version of this book was written in 1983, while I was teach ing at the Department of Systems Science and Mathematics at Washington University in St. Louis. This new edition integrates my subsequent teaching experience gained at the University of Illinois in Urbana-Champaign in 1987, at the Carl-Cranz Gesellschaft in Oberpfaffenhofen in 1987, at the University of California in Berkeley in 1988. In addition to a major rearrangement of the last two Chapters of the first version, this new edition incorporates two additional Chapters at a more elementary level and an exposition of some relevant research findings which have occurred since 1985.
Algebraic And Differential Methods For Nonlinear Control Theory
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Author : Rafael Martínez-Guerra
language : en
Publisher: Springer
Release Date : 2019-01-30
Algebraic And Differential Methods For Nonlinear Control Theory written by Rafael Martínez-Guerra and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-30 with Mathematics categories.
This book is a short primer in engineering mathematics with a view on applications in nonlinear control theory. In particular, it introduces some elementary concepts of commutative algebra and algebraic geometry which offer a set of tools quite different from the traditional approaches to the subject matter. This text begins with the study of elementary set and map theory. Chapters 2 and 3 on group theory and rings, respectively, are included because of their important relation to linear algebra, the group of invertible linear maps (or matrices) and the ring of linear maps of a vector space. Homomorphisms and Ideals are dealt with as well at this stage. Chapter 4 is devoted to the theory of matrices and systems of linear equations. Chapter 5 gives some information on permutations, determinants and the inverse of a matrix. Chapter 6 tackles vector spaces over a field, Chapter 7 treats linear maps resp. linear transformations, and in addition the application in linear control theory of some abstract theorems such as the concept of a kernel, the image and dimension of vector spaces are illustrated. Chapter 8 considers the diagonalization of a matrix and their canonical forms. Chapter 9 provides a brief introduction to elementary methods for solving differential equations and, finally, in Chapter 10, nonlinear control theory is introduced from the point of view of differential algebra.