Analysis And Geometry In Control Theory And Its Applications

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Analysis and Geometry in Control Theory and its Applications

Author : Piernicola Bettiol
Publisher : Springer
ISBN 13 : 3319069179
Total Pages : 235 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Analysis and Geometry in Control Theory and its Applications by : Piernicola Bettiol

Download or read book Analysis and Geometry in Control Theory and its Applications written by Piernicola Bettiol and published by Springer. This book was released on 2015-09-01 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the 1950s control theory has established itself as a major mathematical discipline, particularly suitable for application in a number of research fields, including advanced engineering design, economics and the medical sciences. However, since its emergence, there has been a need to rethink and extend fields such as calculus of variations, differential geometry and nonsmooth analysis, which are closely tied to research on applications. Today control theory is a rich source of basic abstract problems arising from applications, and provides an important frame of reference for investigating purely mathematical issues. In many fields of mathematics, the huge and growing scope of activity has been accompanied by fragmentation into a multitude of narrow specialties. However, outstanding advances are often the result of the quest for unifying themes and a synthesis of different approaches. Control theory and its applications are no exception. Here, the interaction between analysis and geometry has played a crucial role in the evolution of the field. This book collects some recent results, highlighting geometrical and analytical aspects and the possible connections between them. Applications provide the background, in the classical spirit of mutual interplay between abstract theory and problem-solving practice.

Functional Analysis and Control Theory

Author : S. Rolewicz
Publisher : Springer Science & Business Media
ISBN 13 : 9401577587
Total Pages : 539 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Functional Analysis and Control Theory by : S. Rolewicz

Download or read book Functional Analysis and Control Theory written by S. Rolewicz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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 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.

Methods of Algebraic Geometry in Control Theory: Part I

Author : Peter Falb
Publisher : Springer
ISBN 13 : 3319980262
Total Pages : 202 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 202 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

Contemporary Trends in Nonlinear Geometric Control Theory and Its Applications

Author : A. Anzaldo-Meneses
Publisher : World Scientific
ISBN 13 : 9810248415
Total Pages : 495 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Contemporary Trends in Nonlinear Geometric Control Theory and Its Applications by : A. Anzaldo-Meneses

Download or read book Contemporary Trends in Nonlinear Geometric Control Theory and Its Applications written by A. Anzaldo-Meneses and published by World Scientific. This book was released on 2002 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concerns contemporary trends in nonlinear geometric control theory and its applications.

Geometric Control Theory

Author : Velimir Jurdjevic
Publisher : Cambridge University Press
ISBN 13 : 0521495024
Total Pages : 516 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Geometric Control Theory by : Velimir Jurdjevic

Download or read book Geometric Control Theory written by Velimir Jurdjevic and published by Cambridge University Press. This book was released on 1997 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Methods of Algebraic Geometry in Control Theory: Part I

Author : Peter Falb
Publisher : Birkhäuser
ISBN 13 : 9781468492231
Total Pages : 204 pages
Book Rating : 4.4/5 (922 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 Birkhäuser. This book was released on 2012-06-12 with total page 204 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 these notes is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory. I began the development of these notes over fifteen years ago with a series of lectures given to the Control Group at the Lund Institute of Technology in Sweden. Over the following years, I presented the material in courses at Brown several times and must express my appreciation for the feedback (sic!) received from the students. I have attempted throughout to strive for clarity, often making use of constructive methods and giving several proofs of a particular result. Since algebraic geometry draws on so many branches of mathematics and can be dauntingly abstract, it is not easy to convey its beauty and utility to those interested in applications. I hope at least to have stirred the reader to seek a deeper understanding of this beauty and utility in control theory. The first volume dea1s 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).

Methods of Algebraic Geometry in Control Theory: Part II

Author : Peter Falb
Publisher : Springer
ISBN 13 : 3319965743
Total Pages : 390 pages
Book Rating : 4.3/5 (199 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. This book was released on 2018-09-14 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An introduction to the ideas of algebraic geometry in the motivated context of system theory." This describes this two volume work which has been specifically written to serve the needs of researchers and students of systems, control, and applied mathematics. Without sacrificing mathematical rigor, 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 on abstraction. While familiarity with Part I is helpful, it is not essential, since a considerable amount of relevant material is included here. Part I, Scalar Linear Systems and Affine Algebraic Geometry, contains a clear presentation, with an applied flavor , of the core ideas in the algebra-geometric treatment of scalar linear system theory. Part II extends the theory to multivariable systems. After delineating limitations of the scalar theory through carefully chosen examples, the author introduces seven representations of a multivariable linear system and establishes the major results of the underlying theory. Of key importance is a clear, detailed analysis of the structure of the space of linear systems including the full set of equations defining the space. Key topics also covered are the Geometric Quotient Theorem and a highly geometric analysis of both state and output feedback. Prerequisites are the basics of linear algebra, some simple topological notions, the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises, which are an integral part of the exposition throughout, combined with an index and extensive bibliography of related literature make this a valuable classroom tool or good self-study resource. The present, softcover reprint is designed to make this classic textbook available to a wider audience. "The exposition is extremely clear. In order to motivate the general theory, the author presents a number of examples of two or three input-, two-output systems in detail. I highly recommend this excellent book to all those interested in the interplay between control theory and algebraic geometry." —Publicationes Mathematicae, Debrecen "This book is the multivariable counterpart of Methods of Algebraic Geometry in Control Theory, Part I.... In the first volume the simpler single-input–single-output time-invariant linear systems were considered and the corresponding simpler affine algebraic geometry was used as the required prerequisite. Obviously, multivariable systems are more difficult and consequently the algebraic results are deeper and less transparent, but essential in the understanding of linear control theory.... Each chapter contains illustrative examples throughout and terminates with some exercises for further study." —Mathematical Reviews

Information Geometry

Author : Nihat Ay
Publisher : Springer
ISBN 13 : 3319564781
Total Pages : 407 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Information Geometry by : Nihat Ay

Download or read book Information Geometry written by Nihat Ay and published by Springer. This book was released on 2017-08-25 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, information theory, or the foundations of statistics, to statisticians as well as to scientists interested in the mathematical foundations of complex systems.

Nonlinear Analysis, Geometry and Applications

Author : Diaraf Seck
Publisher : Birkhäuser
ISBN 13 : 9783030573386
Total Pages : 462 pages
Book Rating : 4.5/5 (733 download)

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Book Synopsis Nonlinear Analysis, Geometry and Applications by : Diaraf Seck

Download or read book Nonlinear Analysis, Geometry and Applications written by Diaraf Seck and published by Birkhäuser. This book was released on 2021-11-21 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers nineteen papers presented at the first NLAGA-BIRS Symposium, which was held at the Cheikh Anta Diop University in Dakar, Senegal, on June 24–28, 2019. The four-day symposium brought together African experts on nonlinear analysis and geometry and their applications, as well as their international partners, to present and discuss mathematical results in various areas. The main goal of the NLAGA project is to advance and consolidate the development of these mathematical fields in West and Central Africa with a focus on solving real-world problems such as coastal erosion, pollution, and urban network and population dynamics problems. The book addresses a range of topics related to partial differential equations, geometrical analysis of optimal shapes, geometric structures, optimization and optimal transportation, control theory, and mathematical modeling.

Methods of Algebraic Geometry in Control Theory: Part I

Author : Peter Falb
Publisher : Birkhäuser
ISBN 13 : 9781468492217
Total Pages : 0 pages
Book Rating : 4.4/5 (922 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 Birkhäuser. This book was released on 2013-09-14 with total page 0 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 these notes is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory. I began the development of these notes over fifteen years ago with a series of lectures given to the Control Group at the Lund Institute of Technology in Sweden. Over the following years, I presented the material in courses at Brown several times and must express my appreciation for the feedback (sic!) received from the students. I have attempted throughout to strive for clarity, often making use of constructive methods and giving several proofs of a particular result. Since algebraic geometry draws on so many branches of mathematics and can be dauntingly abstract, it is not easy to convey its beauty and utility to those interested in applications. I hope at least to have stirred the reader to seek a deeper understanding of this beauty and utility in control theory. The first volume dea1s 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).

Control Theory from the Geometric Viewpoint

Author : Andrei A. Agrachev
Publisher : Springer
ISBN 13 : 9783642059070
Total Pages : 0 pages
Book Rating : 4.0/5 (59 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. This book was released on 2010-12-05 with total page 0 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.

Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control

Author : Boris S. Mordukhovich
Publisher : Springer Science & Business Media
ISBN 13 : 1461384893
Total Pages : 256 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control by : Boris S. Mordukhovich

Download or read book Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control written by Boris S. Mordukhovich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications NONSMOOTH ANALYSIS AND GEOMETRIC METHODS IN DETERMINISTIC OPTIMAL CONTROL is based on the proceedings of a workshop that was an integral part of the 1992-93 IMA program on "Control Theory. " The purpose of this workshop was to concentrate on powerful mathematical techniques that have been de veloped in deterministic optimal control theory after the basic foundations of the theory (existence theorems, maximum principle, dynamic program ming, sufficiency theorems for sufficiently smooth fields of extremals) were laid out in the 1960s. These advanced techniques make it possible to derive much more detailed information about the structure of solutions than could be obtained in the past, and they support new algorithmic approaches to the calculation of such solutions. We thank Boris S. Mordukhovich and Hector J. Sussmann for organiz ing the workshop and editing the proceedings. We also take this oppor tunity to thank the National Science Foundation and the Army Research Office, whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. v PREFACE This volume contains the proceedings of the workshop on Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control held at the Institute for Mathematics and its Applications on February 8-17, 1993 during a special year devoted to Control Theory and its Applications. The workshop-whose organizing committee consisted of V. J urdjevic, B. S. Mordukhovich, R. T. Rockafellar, and H. J.

Geometric Control Theory and Sub-Riemannian Geometry

Author : Gianna Stefani
Publisher : Springer
ISBN 13 : 331902132X
Total Pages : 385 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Geometric Control Theory and Sub-Riemannian Geometry by : Gianna Stefani

Download or read book Geometric Control Theory and Sub-Riemannian Geometry written by Gianna Stefani and published by Springer. This book was released on 2014-06-05 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Honoring Andrei Agrachev's 60th birthday, this volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume, etc.

Applied Differential Geometry

Author : William L. Burke
Publisher : Cambridge University Press
ISBN 13 : 9780521269292
Total Pages : 440 pages
Book Rating : 4.2/5 (692 download)

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Book Synopsis Applied Differential Geometry by : William L. Burke

Download or read book Applied Differential Geometry written by William L. Burke and published by Cambridge University Press. This book was released on 1985-05-31 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.

Algebraic Geometry For Robotics And Control Theory

Author : Laura Menini
Publisher : World Scientific
ISBN 13 : 1800610475
Total Pages : 615 pages
Book Rating : 4.8/5 (6 download)

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Book Synopsis Algebraic Geometry For Robotics And Control Theory by : Laura Menini

Download or read book Algebraic Geometry For Robotics And Control Theory written by Laura Menini and published by World Scientific. This book was released on 2021-09-02 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of inexpensive and fast computers, coupled with the discovery of efficient algorithms for dealing with polynomial equations, has enabled exciting new applications of algebraic geometry and commutative algebra. Algebraic Geometry for Robotics and Control Theory shows how tools borrowed from these two fields can be efficiently employed to solve relevant problem arising in robotics and control theory.After a brief introduction to various algebraic objects and techniques, the book first covers a wide variety of topics concerning control theory, robotics, and their applications. Specifically this book shows how these computational and theoretical methods can be coupled with classical control techniques to: solve the inverse kinematics of robotic arms; design observers for nonlinear systems; solve systems of polynomial equalities and inequalities; plan the motion of mobile robots; analyze Boolean networks; solve (possibly, multi-objective) optimization problems; characterize the robustness of linear; time-invariant plants; and certify positivity of polynomials.