Geometric Control Theory
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Geometric Control Theory
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Author : Velimir Jurdjevic
language : en
Publisher: Cambridge University Press
Release Date : 1997
Geometric Control Theory written by Velimir Jurdjevic and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Geometric control theory is concerned with the evolution of systems subject to physical laws but having some degree of freedom through which motion is to be controlled. This book describes the mathematical theory inspired by the irreversible nature of time evolving events. The first part of the book deals with the issue of being able to steer the system from any point of departure to any desired destination. The second part deals with optimal control, the question of finding the best possible course. An overlap with mathematical physics is demonstrated by the Maximum principle, a fundamental principle of optimality arising from geometric control, which is applied to time-evolving systems governed by physics as well as to man-made systems governed by controls. Applications are drawn from geometry, mechanics, and control of dynamical systems. The geometric language in which the results are expressed allows clear visual interpretations and makes the book accessible to physicists and engineers as well as to mathematicians.
Control Theory From The Geometric Viewpoint
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Author : Andrei A. Agrachev
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-04-15
Control Theory From The Geometric Viewpoint written by Andrei A. Agrachev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-15 with Language Arts & Disciplines categories.
This book presents some facts and methods of Mathematical Control Theory treated from the geometric viewpoint. It is devoted to finite-dimensional deterministic control systems governed by smooth ordinary differential equations. The problems of controllability, state and feedback equivalence, and optimal control are studied. Some of the topics treated by the authors are covered in monographic or textbook literature for the first time while others are presented in a more general and flexible setting than elsewhere. Although being fundamentally written for mathematicians, the authors make an attempt to reach both the practitioner and the theoretician by blending the theory with applications. They maintain a good balance between the mathematical integrity of the text and the conceptual simplicity that might be required by engineers. It can be used as a text for graduate courses and will become most valuable as a reference work for graduate students and researchers.
Geometric Control Of Mechanical Systems
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Author : Francesco Bullo
language : en
Publisher: Springer
Release Date : 2019-06-12
Geometric Control Of Mechanical Systems written by Francesco Bullo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-12 with Science categories.
The primary emphasis of this book is the modeling, analysis, and control of mechanical systems. The methods and results presented can be applied to a large class of mechanical control systems, including applications in robotics, autonomous vehicle control, and multi-body systems. The book is unique in that it presents a unified, rather than an inclusive, treatment of control theory for mechanical systems. A distinctive feature of the presentation is its reliance on techniques from differential and Riemannian geometry. The book contains extensive examples and exercises, and will be suitable for a growing number of courses in this area. It begins with the detailed mathematical background, proceeding through innovative approaches to physical modeling, analysis, and design techniques. Numerous examples illustrate the proposed methods and results, while the many exercises test basic knowledge and introduce topics not covered in the main body of the text. The audience of this book consists of two groups. The first group is comprised of graduate students in engineering or mathematical sciences who wish to learn the basics of geometric mechanics, nonlinear control theory, and control theory for mechanical systems. Readers will be able to immediately begin exploring the research literature on these subjects. The second group consists of researchers in mechanics and control theory. Nonlinear control theoreticians will find explicit links between concepts in geometric mechanics and nonlinear control theory. Researchers in mechanics will find an overview of topics in control theory that have relevance to mechanics.
Geometric Optimal Control
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Author : Heinz Schättler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-26
Geometric Optimal Control written by Heinz Schättler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-26 with Mathematics categories.
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.
Linear Multivariable Control A Geometric Approach
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Author : W. M. Wonham
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Linear Multivariable Control A Geometric Approach written by W. M. Wonham and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
In writing this monograph my aim has been to present a "geometric" 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 mathemati cians with some previous acquaintance with control problems. The present edition of this book is a revision of the preliminary version, published in 1974 as a Springer-Verlag "Lecture Notes" volume; and some of the remarks to follow are repeated from the original preface. The label "geometric" in the title is applied for several reasons. First and obviously, the setting is linear state space and the mathematics chiefly linear algebra in abstract (geometric) style. The basic ideas are the familiar system concepts of controllability and observability, thought of as geometric 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 secondly and of greater interest, the geometric setting rather quickly suggested new methods of attacking synthesis which have proved to be intuitive and econo mical; they are also easily reduced to matrix arithmetic as soon as you want to compute.
Methods Of Algebraic Geometry In Control Theory Part I
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Author : Peter Falb
language : en
Publisher: Birkhäuser
Release Date : 1990-07-01
Methods Of Algebraic Geometry In Control Theory Part I written by Peter Falb and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-07-01 with Mathematics categories.
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).
Nonholonomic Mechanics And Control
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Author : A.M. Bloch
language : en
Publisher: Springer
Release Date : 2015-11-05
Nonholonomic Mechanics And Control written by A.M. Bloch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-05 with Science categories.
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.
Differential Geometric Control Theory
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Author : Roger W. Brockett
language : en
Publisher: Birkhauser
Release Date : 1983
Differential Geometric Control Theory written by Roger W. Brockett and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
Control Theory For Linear Systems
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Author : Harry L. Trentelman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Control Theory For Linear Systems written by Harry L. Trentelman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
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.