Geometric Methods In System Theory

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Geometric Methods in System Theory

Author : D.Q. Mayne
Publisher : Springer Science & Business Media
ISBN 13 : 9401026750
Total Pages : 322 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Geometric Methods in System Theory by : D.Q. Mayne

Download or read book Geometric Methods in System Theory written by D.Q. Mayne and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Methods in System Theory In automatic control there are a large number of applications of a fairly simple type for which the motion of the state variables is not free to evolve in a vector space but rather must satisfy some constraints. Examples are numerous; in a switched, lossless electrical network energy is conserved and the state evolves on an ellipsoid surface defined by x'Qx equals a constant; in the control of finite state, continuous time, Markov processes the state evolves on the set x'x = 1, xi ~ O. The control of rigid body motions and trajectory control leads to problems of this type. There has been under way now for some time an effort to build up enough control theory to enable one to treat these problems in a more or less routine way. It is important to emphasise that the ordinary vector space-linear theory often gives the wrong insight and thus should not be relied upon.

Geometrical Methods in the Theory of Ordinary Differential Equations

Author : V.I. Arnold
Publisher : Springer Science & Business Media
ISBN 13 : 1461210372
Total Pages : 366 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Geometrical Methods in the Theory of Ordinary Differential Equations by : V.I. Arnold

Download or read book Geometrical Methods in the Theory of Ordinary Differential Equations written by V.I. Arnold and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. Much of this progress is represented in this revised, expanded edition, including such topics as the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems, and the Neistadt theory. In the selection of material for this book, the author explains basic ideas and methods applicable to the study of differential equations. Special efforts were made to keep the basic ideas free from excessive technicalities. Thus the most fundamental questions are considered in great detail, while of the more special and difficult parts of the theory have the character of a survey. Consequently, the reader needs only a general mathematical knowledge to easily follow this text. It is directed to mathematicians, as well as all users of the theory of differential equations.

Methods of Algebraic Geometry in Control Theory: Part I

Author : Peter Falb
Publisher : Springer
ISBN 13 : 3319980262
Total Pages : 211 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Methods of Algebraic Geometry in Control Theory: Part I by : Peter Falb

Download or read book Methods of Algebraic Geometry in Control Theory: Part I written by Peter Falb and published by Springer. This book was released on 2018-08-25 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An introduction to the ideas of algebraic geometry in the motivated context of system theory." Thus the author describes his textbook that has been specifically written to serve the needs of students of systems and control. Without sacrificing mathematical care, the author makes the basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis is on constructive methods and clarity rather than abstraction. The student will find here a clear presentation with an applied flavor, of the core ideas in the algebra-geometric treatment of scalar linear system theory. The author introduces the four representations of a scalar linear system and establishes the major results of a similar theory for multivariable systems appearing in a succeeding volume (Part II: Multivariable Linear Systems and Projective Algebraic Geometry). Prerequisites are the basics of linear algebra, some simple notions from topology and the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises are an integral part of the treatment and are used where relevant in the main body of the text. The present, softcover reprint is designed to make this classic textbook available to a wider audience. "This book is a concise development of affine algebraic geometry together with very explicit links to the applications...[and] should address a wide community of readers, among pure and applied mathematicians." —Monatshefte für Mathematik

Geometrical Methods for the Theory of Linear Systems

Author : C.I. Byrnes
Publisher : Springer Science & Business Media
ISBN 13 : 9400990820
Total Pages : 320 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Geometrical Methods for the Theory of Linear Systems by : C.I. Byrnes

Download or read book Geometrical Methods for the Theory of Linear Systems written by C.I. Byrnes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures contained in this book were presented at Harvard University in June 1979. The workshop at which they were presented was the third such on algebro-geometric methods. The first was held in 1973 in London and the emphasis was largely on geometric methods. The second was held at Ames Research Center-NASA in 1976. There again the emphasis was on geometric methods, but algebraic geometry was becoming a dominant theme. In the two years after the Ames meeting there was tremendous growth in the applications of algebraic geometry to systems theory and it was becoming clear that much of the algebraic systems theory was very closely related to the geometric systems theory. On this basis we felt that this was the right time to devote a workshop to the applications of algebra and algebraic geometry to linear systems theory. The lectures contained in this volume represent all but one of the tutorial lectures presented at the workshop. The lec ture of Professor Murray Wonham is not contained in this volume and we refer the interested to the archival literature. This workshop was jointly sponsored by a grant from Ames Research Center-NASA and a grant from the Advanced Study Institute Program of NATO. We greatly appreciate the financial support rendered by these two organizations. The American Mathematical Society hosted this meeting as part of their Summer Seminars in Applied Mathematics and will publish the companion volume of con tributed papers.

Control Theory from the Geometric Viewpoint

Author : Andrei A. Agrachev
Publisher : Springer Science & Business Media
ISBN 13 : 3662064049
Total Pages : 415 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Control Theory from the Geometric Viewpoint by : Andrei A. Agrachev

Download or read book Control Theory from the Geometric Viewpoint written by Andrei A. Agrachev and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some facts and methods of the Mathematical Control Theory treated from the geometric point of view. The book is mainly based on graduate courses given by the first coauthor in the years 2000-2001 at the International School for Advanced Studies, Trieste, Italy. Mathematical prerequisites are reduced to standard courses of Analysis and Linear Algebra plus some basic Real and Functional Analysis. No preliminary knowledge of Control Theory or Differential Geometry is required. What this book is about? The classical deterministic physical world is described by smooth dynamical systems: the future in such a system is com pletely determined by the initial conditions. Moreover, the near future changes smoothly with the initial data. If we leave room for "free will" in this fatalistic world, then we come to control systems. We do so by allowing certain param eters of the dynamical system to change freely at every instant of time. That is what we routinely do in real life with our body, car, cooker, as well as with aircraft, technological processes etc. We try to control all these dynamical systems! Smooth dynamical systems are governed by differential equations. In this book we deal only with finite dimensional systems: they are governed by ordi nary differential equations on finite dimensional smooth manifolds. A control system for us is thus a family of ordinary differential equations. The family is parametrized by control parameters.

Geometric Theory of Dynamical Systems

Author : J. Jr. Palis
Publisher : Springer Science & Business Media
ISBN 13 : 1461257034
Total Pages : 208 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Geometric Theory of Dynamical Systems by : J. Jr. Palis

Download or read book Geometric Theory of Dynamical Systems written by J. Jr. Palis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: ... cette etude qualitative (des equations difj'erentielles) aura par elle-m me un inter t du premier ordre ... HENRI POINCARE, 1881. We present in this book a view of the Geometric Theory of Dynamical Systems, which is introductory and yet gives the reader an understanding of some of the basic ideas involved in two important topics: structural stability and genericity. This theory has been considered by many mathematicians starting with Poincare, Liapunov and Birkhoff. In recent years some of its general aims were established and it experienced considerable development. More than two decades passed between two important events: the work of Andronov and Pontryagin (1937) introducing the basic concept of structural stability and the articles of Peixoto (1958-1962) proving the density of stable vector fields on surfaces. It was then that Smale enriched the theory substantially by defining as a main objective the search for generic and stable properties and by obtaining results and proposing problems of great relevance in this context. In this same period Hartman and Grobman showed that local stability is a generic property. Soon after this Kupka and Smale successfully attacked the problem for periodic orbits. We intend to give the reader the flavour of this theory by means of many examples and by the systematic proof of the Hartman-Grobman and the Stable Manifold Theorems (Chapter 2), the Kupka-Smale Theorem (Chapter 3) and Peixoto's Theorem (Chapter 4). Several ofthe proofs we give vii Introduction Vlll are simpler than the original ones and are open to important generalizations.

Algebraic and Geometric Methods in Linear Systems Theory

Author : Christopher I. Byrnes
Publisher : American Mathematical Soc.
ISBN 13 : 9780821811184
Total Pages : 327 pages
Book Rating : 4.8/5 (111 download)

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Book Synopsis Algebraic and Geometric Methods in Linear Systems Theory by : Christopher I. Byrnes

Download or read book Algebraic and Geometric Methods in Linear Systems Theory written by Christopher I. Byrnes and published by American Mathematical Soc.. This book was released on 1980 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometric Control of Mechanical Systems

Author : Francesco Bullo
Publisher : Springer
ISBN 13 : 1489972765
Total Pages : 727 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Geometric Control of Mechanical Systems by : Francesco Bullo

Download or read book Geometric Control of Mechanical Systems written by Francesco Bullo and published by Springer. This book was released on 2019-06-12 with total page 727 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of analysis and control of mechanical systems using differential geometry is flourishing. This book collects many results over the last decade and provides a comprehensive introduction to the area.

Linear Multivariable Control

Author : W. M. Wonham
Publisher : Springer Science & Business Media
ISBN 13 : 3662226731
Total Pages : 357 pages
Book Rating : 4.6/5 (622 download)

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Book Synopsis Linear Multivariable Control by : W. M. Wonham

Download or read book Linear Multivariable Control written by W. M. Wonham and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: In writing this monograph my objective is to present arecent, 'geometrie' approach to the structural synthesis of multivariable control systems that are linear, time-invariant, and of finite dynamic order. The book is addressed to graduate students specializing in control, to engineering scientists engaged in control systems research and development, and to mathematicians with some previous acquaintance with control problems. The label 'geometrie' is applied for several reasons. First and obviously, the setting is linear state space and the mathematics chiefly linear algebra in abstract (geometrie) style. The basic ideas are the familiar system concepts of controllability and observability, thought of as geometrie properties of distinguished state subspaces. Indeed, the geometry was first brought in out of revulsion against the orgy of matrix manipulation which linear control theory mainly consisted of, not so long ago. But secondlyand of greater interest, the geometrie setting rather quickly suggested new methods of attacking synthesis which have proved to be intuitive and economical; they are also easily reduced to matrix arith metic as soonas you want to compute. The essence of the 'geometrie' approach is just this: instead of looking directly for a feedback laW (say u = Fx) which would solve your synthesis problem if a solution exists, first characterize solvability as a verifiable property of some constructible state subspace, say J. Then, if all is weIl, you may calculate F from J quite easily.

Geometric methods in system theory

Author : D. Q. Mayne
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (476 download)

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Book Synopsis Geometric methods in system theory by : D. Q. Mayne

Download or read book Geometric methods in system theory written by D. Q. Mayne and published by . This book was released on 1973 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

GEOMETRIC METHODS IN SYSTEM THEORY- PROCEEDINGS OF THE NATO ADVANCED STUDY INSTITUTE.

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (846 download)

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Book Synopsis GEOMETRIC METHODS IN SYSTEM THEORY- PROCEEDINGS OF THE NATO ADVANCED STUDY INSTITUTE. by :

Download or read book GEOMETRIC METHODS IN SYSTEM THEORY- PROCEEDINGS OF THE NATO ADVANCED STUDY INSTITUTE. written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Reduction of Nonlinear Control Systems

Author : V.I. Elkin
Publisher : Springer Science & Business Media
ISBN 13 : 9401146179
Total Pages : 259 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Reduction of Nonlinear Control Systems by : V.I. Elkin

Download or read book Reduction of Nonlinear Control Systems written by V.I. Elkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in science and technology necessitate the use of increasingly-complicated dynamic control processes. Undoubtedly, sophisticated mathematical models are also concurrently elaborated for these processes. In particular, linear dynamic control systems iJ = Ay + Bu, y E M C ]Rn, U E ]RT, (1) where A and B are constants, are often abandoned in favor of nonlinear dynamic control systems (2) which, in addition, contain a large number of equations. The solution of problems for multidimensional nonlinear control systems en counters serious difficulties, which are both mathematical and technical in nature. Therefore it is imperative to develop methods of reduction of nonlinear systems to a simpler form, for example, decomposition into systems of lesser dimension. Approaches to reduction are diverse, in particular, techniques based on approxi mation methods. In this monograph, we elaborate the most natural and obvious (in our opinion) approach, which is essentially inherent in any theory of math ematical entities, for instance, in the theory of linear spaces, theory of groups, etc. Reduction in our interpretation is based on assigning to the initial object an isomorphic object, a quotient object, and a subobject. In the theory of linear spaces, for instance, reduction consists in reducing to an isomorphic linear space, quotient space, and subspace. Strictly speaking, the exposition of any mathemat ical theory essentially begins with the introduction of these reduced objects and determination of their basic properties in relation to the initial object.

Geometric Methods in System Theory

Author : Roger W. Brockett
Publisher :
ISBN 13 :
Total Pages : 314 pages
Book Rating : 4.:/5 (233 download)

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Book Synopsis Geometric Methods in System Theory by : Roger W. Brockett

Download or read book Geometric Methods in System Theory written by Roger W. Brockett and published by . This book was released on 1973 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Observer Design for Nonlinear Dynamical Systems

Author : Driss Boutat
Publisher : Springer Nature
ISBN 13 : 303073742X
Total Pages : 192 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Observer Design for Nonlinear Dynamical Systems by : Driss Boutat

Download or read book Observer Design for Nonlinear Dynamical Systems written by Driss Boutat and published by Springer Nature. This book was released on 2021-07-02 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a differential geometric method for designing nonlinear observers for multiple types of nonlinear systems, including single and multiple outputs, fully and partially observable systems, and regular and singular dynamical systems. It is an exposition of achievements in nonlinear observer normal forms. The book begins by discussing linear systems, introducing the concept of observability and observer design, and then explains the difficulty of those problems for nonlinear systems. After providing foundational information on the differential geometric method, the text shows how to use the method to address observer design problems. It presents methods for a variety of systems. The authors employ worked examples to illustrate the ideas presented. Observer Design for Nonlinear Dynamical Systems will be of interest to researchers, graduate students, and industrial professionals working with control of mechanical and dynamical systems.

Geometric Methods and Optimization Problems

Author : Vladimir Boltyanski
Publisher : Springer Science & Business Media
ISBN 13 : 1461553199
Total Pages : 438 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Geometric Methods and Optimization Problems by : Vladimir Boltyanski

Download or read book Geometric Methods and Optimization Problems written by Vladimir Boltyanski and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: VII Preface In many fields of mathematics, geometry has established itself as a fruitful method and common language for describing basic phenomena and problems as well as suggesting ways of solutions. Especially in pure mathematics this is ob vious and well-known (examples are the much discussed interplay between lin ear algebra and analytical geometry and several problems in multidimensional analysis). On the other hand, many specialists from applied mathematics seem to prefer more formal analytical and numerical methods and representations. Nevertheless, very often the internal development of disciplines from applied mathematics led to geometric models, and occasionally breakthroughs were b~ed on geometric insights. An excellent example is the Klee-Minty cube, solving a problem of linear programming by transforming it into a geomet ric problem. Also the development of convex programming in recent decades demonstrated the power of methods that evolved within the field of convex geometry. The present book focuses on three applied disciplines: control theory, location science and computational geometry. It is our aim to demonstrate how methods and topics from convex geometry in a wider sense (separation theory of convex cones, Minkowski geometry, convex partitionings, etc.) can help to solve various problems from these disciplines.

Methods of Algebraic Geometry in Control Theory: Part II

Author : Peter Falb
Publisher : Springer Science & Business Media
ISBN 13 : 9780817641139
Total Pages : 408 pages
Book Rating : 4.6/5 (411 download)

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Book Synopsis Methods of Algebraic Geometry in Control Theory: Part II by : Peter Falb

Download or read book Methods of Algebraic Geometry in Control Theory: Part II written by Peter Falb and published by Springer Science & Business Media. This book was released on 1990 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, be viewed as the study of the structure and properties of the solutions of systems of algebraic equations. The aim of this book is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory" .* The development which culminated with this volume began over twenty-five years ago with a series of lectures at the control group of the Lund Institute of Technology in Sweden. I have sought throughout to strive for clarity, often using constructive methods and giving several proofs of a particular result as well as many examples. The first volume dealt with the simplest control systems (i.e., single input, single output linear time-invariant systems) and with the simplest algebraic geometry (i.e., affine algebraic geometry). While this is quite satisfactory and natural for scalar systems, the study of multi-input, multi-output linear time invariant control systems requires projective algebraic geometry. Thus, this second volume deals with multi-variable linear systems and pro jective algebraic geometry. The results are deeper and less transparent, but are also quite essential to an understanding of linear control theory. A review of * From the Preface to Part 1. viii Preface the scalar theory is included along with a brief summary of affine algebraic geometry (Appendix E).

Mathematical Methods for System Theory

Author : Federico Gentili
Publisher : World Scientific
ISBN 13 : 9789810233341
Total Pages : 584 pages
Book Rating : 4.2/5 (333 download)

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Book Synopsis Mathematical Methods for System Theory by : Federico Gentili

Download or read book Mathematical Methods for System Theory written by Federico Gentili and published by World Scientific. This book was released on 1998 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers selected topics in geometry, algebra, calculus and probability theory. It contains the basic mathematical notions required by a first course in system theory for engineering and applied mathematics students. It is the first book to provide a self-contained and precise account of all the major mathematical methods and concepts relevant to the study of system theory.