Geometric Control Theory

Author : Velimir Jurdjevic
Publisher : Cambridge University Press
Page : 516 pages
File Size : 48,7 Mb
Release : 1997
Category : Mathematics
ISBN : 9780521495028

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Geometric Control Theory by Velimir Jurdjevic Pdf

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.

Author : Andrei A. Agrachev,Yuri Sachkov
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 45,8 Mb
Release : 2013-03-14
Category : Science
ISBN : 9783662064047

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Control Theory from the Geometric Viewpoint by Andrei A. Agrachev,Yuri Sachkov Pdf

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.

Author : Francesco Bullo,Andrew D. Lewis
Publisher : Springer
Page : 727 pages
File Size : 44,8 Mb
Release : 2019-06-12
Category : Science
ISBN : 9781489972767

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Geometric Control of Mechanical Systems by Francesco Bullo,Andrew D. Lewis Pdf

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.

Author : Roger W. Brockett
Publisher : Birkhauser
Page : 360 pages
File Size : 42,8 Mb
Release : 1983
Category : Mathematics
ISBN : UOM:39015049367405

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Differential Geometric Control Theory by Roger W. Brockett Pdf

Author : W. M. Wonham
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 49,7 Mb
Release : 2013-11-21
Category : Science
ISBN : 9783662226735

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Linear Multivariable Control by W. M. Wonham Pdf

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.

Author : A. Anzaldo-Meneses
Publisher : World Scientific
Page : 495 pages
File Size : 47,6 Mb
Release : 2002
Category : Mathematics
ISBN : 9789810248413

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

Concerns contemporary trends in nonlinear geometric control theory and its applications.

Author : Heinz Schättler,Urszula Ledzewicz
Publisher : Springer Science & Business Media
Page : 652 pages
File Size : 55,5 Mb
Release : 2012-06-26
Category : Mathematics
ISBN : 9781461438342

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Geometric Optimal Control by Heinz Schättler,Urszula Ledzewicz Pdf

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.

Author : Gianna Stefani,Ugo Boscain,Jean-Paul Gauthier,Andrey Sarychev,Mario Sigalotti
Publisher : Springer
Page : 385 pages
File Size : 52,6 Mb
Release : 2014-06-05
Category : Mathematics
ISBN : 9783319021324

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Geometric Control Theory and Sub-Riemannian Geometry by Gianna Stefani,Ugo Boscain,Jean-Paul Gauthier,Andrey Sarychev,Mario Sigalotti Pdf

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.

Author : Peter Falb
Publisher : Springer
Page : 202 pages
File Size : 46,6 Mb
Release : 2018-08-25
Category : Mathematics
ISBN : 9783319980263

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

"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

Author : A.M. Bloch
Publisher : Springer
Page : 565 pages
File Size : 53,7 Mb
Release : 2015-11-05
Category : Science
ISBN : 9781493930173

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Nonholonomic Mechanics and Control by A.M. Bloch Pdf

This book explores connections between control theory and geometric mechanics. The author links control theory with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations, and in particular with the theory of mechanical systems subject to motion constraints. The synthesis is appropriate as there is a rich connection between mechanics and nonlinear control theory. The book provides a unified treatment of nonlinear control theory and constrained mechanical systems that incorporates material not available in other recent texts. The book benefits graduate students and researchers in the area who want to enhance their understanding and enhance their techniques.

Author : Robert Hermann
Publisher : Unknown
Page : 610 pages
File Size : 40,5 Mb
Release : 1979
Category : Mathematics
ISBN : 0915692295

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Cartanian Geometry, Nonlinear Waves, and Control Theory by Robert Hermann Pdf

Author : Clyde Martin,Robert Hermann
Publisher : Unknown
Page : 584 pages
File Size : 42,6 Mb
Release : 1977
Category : Control theory
ISBN : UOM:39015049061743

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The 1976 Ames Research Center (NASA) Conference on Geometric Control Theory by Clyde Martin,Robert Hermann Pdf

Author : Robert Hermann
Publisher : Math Science Press
Page : 464 pages
File Size : 41,6 Mb
Release : 1974
Category : Mathematics
ISBN : STANFORD:36105031803195

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Geometric Structure of Systems-control Theory and Physics by Robert Hermann Pdf

Author : M.I. Zelikin
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 46,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662041369

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Control Theory and Optimization I by M.I. Zelikin Pdf

The only monograph on the topic, this book concerns geometric methods in the theory of differential equations with quadratic right-hand sides, closely related to the calculus of variations and optimal control theory. Based on the author’s lectures, the book is addressed to undergraduate and graduate students, and scientific researchers.

Author : Harry L. Trentelman,Anton A. Stoorvogel,Malo Hautus
Publisher : Springer Science & Business Media
Page : 393 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781447103394

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Control Theory for Linear Systems by Harry L. Trentelman,Anton A. Stoorvogel,Malo Hautus Pdf

Control Theory for Linear Systems deals with the mathematical theory of feedback control of linear systems. It treats a wide range of control synthesis problems for linear state space systems with inputs and outputs. The book provides a treatment of these problems using state space methods, often with a geometric flavour. Its subject matter ranges from controllability and observability, stabilization, disturbance decoupling, and tracking and regulation, to linear quadratic regulation, H2 and H-infinity control, and robust stabilization. Each chapter of the book contains a series of exercises, intended to increase the reader's understanding of the material. Often, these exercises generalize and extend the material treated in the regular text.