Control Theory From The Geometric Viewpoint

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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.

Introduction to Geometric Control

Author : Yuri Sachkov
Publisher : Springer Nature
ISBN 13 : 3031020707
Total Pages : 176 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Introduction to Geometric Control by : Yuri Sachkov

Download or read book Introduction to Geometric Control written by Yuri Sachkov and published by Springer Nature. This book was released on 2022-07-02 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an enhanced, English version of the Russian edition, published in early 2021 and is appropriate for an introductory course in geometric control theory. The concise presentation provides an accessible treatment of the subject for advanced undergraduate and graduate students in theoretical and applied mathematics, as well as to experts in classic control theory for whom geometric methods may be introduced. Theory is accompanied by characteristic examples such as stopping a train, motion of mobile robot, Euler elasticae, Dido's problem, and rolling of the sphere on the plane. Quick foundations to some recent topics of interest like control on Lie groups and sub-Riemannian geometry are included. Prerequisites include only a basic knowledge of calculus, linear algebra, and ODEs; preliminary knowledge of control theory is not assumed. The applications problems-oriented approach discusses core subjects and encourages the reader to solve related challenges independently. Highly-motivated readers can acquire working knowledge of geometric control techniques and progress to studying control problems and more comprehensive books on their own. Selected sections provide exercises to assist in deeper understanding of the material. Controllability and optimal control problems are considered for nonlinear nonholonomic systems on smooth manifolds, in particular, on Lie groups. For the controllability problem, the following questions are considered: controllability of linear systems, local controllability of nonlinear systems, Nagano–Sussmann Orbit theorem, Rashevskii–Chow theorem, Krener's theorem. For the optimal control problem, Filippov's theorem is stated, invariant formulation of Pontryagin maximum principle on manifolds is given, second-order optimality conditions are discussed, and the sub-Riemannian problem is studied in detail. Pontryagin maximum principle is proved for sub-Riemannian problems, solution to the sub-Riemannian problems on the Heisenberg group, the group of motions of the plane, and the Engel group is described.

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.

Feedback Control Theory

Author : John C. Doyle
Publisher : Courier Corporation
ISBN 13 : 0486318338
Total Pages : 264 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Feedback Control Theory by : John C. Doyle

Download or read book Feedback Control Theory written by John C. Doyle and published by Courier Corporation. This book was released on 2013-04-09 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: An excellent introduction to feedback control system design, this book offers a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems. Its explorations of recent developments in the field emphasize the relationship of new procedures to classical control theory, with a focus on single input and output systems that keeps concepts accessible to students with limited backgrounds. The text is geared toward a single-semester senior course or a graduate-level class for students of electrical engineering. The opening chapters constitute a basic treatment of feedback design. Topics include a detailed formulation of the control design program, the fundamental issue of performance/stability robustness tradeoff, and the graphical design technique of loopshaping. Subsequent chapters extend the discussion of the loopshaping technique and connect it with notions of optimality. Concluding chapters examine controller design via optimization, offering a mathematical approach that is useful for multivariable systems.

Mathematical Control Theory

Author : Eduardo D. Sontag
Publisher : Springer Science & Business Media
ISBN 13 : 1461205778
Total Pages : 543 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Mathematical Control Theory by : Eduardo D. Sontag

Download or read book Mathematical Control Theory written by Eduardo D. Sontag and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.

Geometric Structure of Systems-control Theory and Physics

Author : Robert Hermann
Publisher : Math Science Press
ISBN 13 :
Total Pages : 464 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Geometric Structure of Systems-control Theory and Physics by : Robert Hermann

Download or read book Geometric Structure of Systems-control Theory and Physics written by Robert Hermann and published by Math Science Press. This book was released on 1974 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Complex Functions

Author : Gareth A. Jones
Publisher : Cambridge University Press
ISBN 13 : 9780521313667
Total Pages : 362 pages
Book Rating : 4.3/5 (136 download)

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Book Synopsis Complex Functions by : Gareth A. Jones

Download or read book Complex Functions written by Gareth A. Jones and published by Cambridge University Press. This book was released on 1987-03-19 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: An elementary account of many aspects of classical complex function theory, including Mobius transformations, elliptic functions, Riemann surfaces, Fuchsian groups and modular functions. The book is based on lectures given to advanced undergraduate students and is well suited as a textbook for a second course in complex function theory.

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.

Three-dimensional Computer Vision

Author : Olivier Faugeras
Publisher : MIT Press
ISBN 13 : 9780262061582
Total Pages : 712 pages
Book Rating : 4.0/5 (615 download)

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Book Synopsis Three-dimensional Computer Vision by : Olivier Faugeras

Download or read book Three-dimensional Computer Vision written by Olivier Faugeras and published by MIT Press. This book was released on 1993 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph by one of the world's leading vision researchers provides a thorough, mathematically rigorous exposition of a broad and vital area in computer vision: the problems and techniques related to three-dimensional (stereo) vision and motion. The emphasis is on using geometry to solve problems in stereo and motion, with examples from navigation and object recognition. Faugeras takes up such important problems in computer vision as projective geometry, camera calibration, edge detection, stereo vision (with many examples on real images), different kinds of representations and transformations (especially 3-D rotations), uncertainty and methods of addressing it, and object representation and recognition. His theoretical account is illustrated with the results of actual working programs.Three-Dimensional Computer Vision proposes solutions to problems arising from a specific robotics scenario in which a system must perceive and act. Moving about an unknown environment, the system has to avoid static and mobile obstacles, build models of objects and places in order to be able to recognize and locate them, and characterize its own motion and that of moving objects, by providing descriptions of the corresponding three-dimensional motions. The ideas generated, however, can be used indifferent settings, resulting in a general book on computer vision that reveals the fascinating relationship of three-dimensional geometry and the imaging process.

Cartanian Geometry, Nonlinear Waves, and Control Theory

Author : Robert Hermann
Publisher :
ISBN 13 : 9780915692293
Total Pages : 610 pages
Book Rating : 4.6/5 (922 download)

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Book Synopsis Cartanian Geometry, Nonlinear Waves, and Control Theory by : Robert Hermann

Download or read book Cartanian Geometry, Nonlinear Waves, and Control Theory written by Robert Hermann and published by . This book was released on 1979 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Geometric Optimal Control

Author : Heinz Schättler
Publisher : Springer Science & Business Media
ISBN 13 : 1461438349
Total Pages : 652 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Geometric Optimal Control by : Heinz Schättler

Download or read book Geometric Optimal Control written by Heinz Schättler and published by Springer Science & Business Media. This book was released on 2012-06-26 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. The emphasis is on the geometric aspects of the theory and on illustrating how these methods can be used to solve optimal control problems. It provides tools and techniques that go well beyond standard procedures and can be used to obtain a full understanding of the global structure of solutions for the underlying problem. The text includes a large number and variety of fully worked out examples that range from the classical problem of minimum surfaces of revolution to cancer treatment for novel therapy approaches. All these examples, in one way or the other, illustrate the power of geometric techniques and methods. The versatile text contains material on different levels ranging from the introductory and elementary to the advanced. Parts of the text can be viewed as a comprehensive textbook for both advanced undergraduate and all level graduate courses on optimal control in both mathematics and engineering departments. The text moves smoothly from the more introductory topics to those parts that are in a monograph style were advanced topics are presented. While the presentation is mathematically rigorous, it is carried out in a tutorial style that makes the text accessible to a wide audience of researchers and students from various fields, including the mathematical sciences and engineering. Heinz Schättler is an Associate Professor at Washington University in St. Louis in the Department of Electrical and Systems Engineering, Urszula Ledzewicz is a Distinguished Research Professor at Southern Illinois University Edwardsville in the Department of Mathematics and Statistics.

Mathematical Control Theory

Author : John B. Baillieul
Publisher : Springer Science & Business Media
ISBN 13 : 1461214165
Total Pages : 389 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Mathematical Control Theory by : John B. Baillieul

Download or read book Mathematical Control Theory written by John B. Baillieul and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume on mathematical control theory contains high quality articles covering the broad range of this field. The internationally renowned authors provide an overview of many different aspects of control theory, offering a historical perspective while bringing the reader up to the very forefront of current research.

Calculus of Variations and Optimal Control Theory

Author : Daniel Liberzon
Publisher : Princeton University Press
ISBN 13 : 0691151873
Total Pages : 255 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Calculus of Variations and Optimal Control Theory by : Daniel Liberzon

Download or read book Calculus of Variations and Optimal Control Theory written by Daniel Liberzon and published by Princeton University Press. This book was released on 2012 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control

Geometric and Topological Inference

Author : Jean-Daniel Boissonnat
Publisher : Cambridge University Press
ISBN 13 : 1108419399
Total Pages : 247 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Geometric and Topological Inference by : Jean-Daniel Boissonnat

Download or read book Geometric and Topological Inference written by Jean-Daniel Boissonnat and published by Cambridge University Press. This book was released on 2018-09-27 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.

Nonlinear Systems Analysis

Author : M. Vidyasagar
Publisher : SIAM
ISBN 13 : 9780898719185
Total Pages : 515 pages
Book Rating : 4.7/5 (191 download)

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Book Synopsis Nonlinear Systems Analysis by : M. Vidyasagar

Download or read book Nonlinear Systems Analysis written by M. Vidyasagar and published by SIAM. This book was released on 2002-01-01 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebra and Applications 2

Author : Abdenacer Makhlouf
Publisher : John Wiley & Sons
ISBN 13 : 1789450187
Total Pages : 338 pages
Book Rating : 4.7/5 (894 download)

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Book Synopsis Algebra and Applications 2 by : Abdenacer Makhlouf

Download or read book Algebra and Applications 2 written by Abdenacer Makhlouf and published by John Wiley & Sons. This book was released on 2021-12-29 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the second of three volumes specifically focusing on algebra and its applications. Algebra and Applications 2 centers on the increasing role played by combinatorial algebra and Hopf algebras, including an overview of the basic theories on non-associative algebras, operads and (combinatorial) Hopf algebras. The chapters are written by recognized experts in the field, providing insight into new trends, as well as a comprehensive introduction to the theory. The book incorporates self-contained surveys with the main results, applications and perspectives. The chapters in this volume cover a wide variety of algebraic structures and their related topics. Alongside the focal topic of combinatorial algebra and Hopf algebras, non-associative algebraic structures in iterated integrals, chronological calculus, differential equations, numerical methods, control theory, non-commutative symmetric functions, Lie series, descent algebras, Butcher groups, chronological algebras, Magnus expansions and Rota–Baxter algebras are explored. Algebra and Applications 2 is of great interest to graduate students and researchers. Each chapter combines some of the features of both a graduate level textbook and of research level surveys.