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Unsolved Problems in Mathematical Systems and Control Theory

Author : Vincent D. Blondel

Publisher : Princeton University Press

Page : 351 pages

File Size : 46,4 MB

Release : 2009-04-11

Category : Mathematics

ISBN : 1400826152

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Book Description

This book provides clear presentations of more than sixty important unsolved problems in mathematical systems and control theory. Each of the problems included here is proposed by a leading expert and set forth in an accessible manner. Covering a wide range of areas, the book will be an ideal reference for anyone interested in the latest developments in the field, including specialists in applied mathematics, engineering, and computer science. The book consists of ten parts representing various problem areas, and each chapter sets forth a different problem presented by a researcher in the particular area and in the same way: description of the problem, motivation and history, available results, and bibliography. It aims not only to encourage work on the included problems but also to suggest new ones and generate fresh research. The reader will be able to submit solutions for possible inclusion on an online version of the book to be updated quarterly on the Princeton University Press website, and thus also be able to access solutions, updated information, and partial solutions as they are developed.



Mathematical Problems of Control Theory

Author : Gennadi? Alekseevich Leonov

Publisher : World Scientific

Page : 188 pages

File Size : 10,67 MB

Release : 2001

Category : Science

ISBN : 9789812799852

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Book Description

This book shows clearly how the study of concrete control systems has motivated the development of the mathematical tools needed for solving such problems. In many cases, by using this apparatus, far-reaching generalizations have been made, and its further development will have an important effect on many fields of mathematics. In the book a way is demonstrated in which the study of the Watt flyball governor has given rise to the theory of stability of motion. The criteria of controllability, observability, and stabilization are stated. Analysis is made of dynamical systems, which describe an autopilot, spacecraft orientation system, controllers of a synchronous electric machine, and phase-locked loops. The Aizerman and Brockett problems are discussed and an introduction to the theory of discrete control systems is given. Contents: The Watt Governor and the Mathematical Theory of Stability of Motion; Linear Electric Circuits. Transfer Functions and Frequency Responses of Linear Blocks; Controllability, Observability, Stabilization; Two-Dimensional Control Systems. Phase Portraits; Discrete Systems; The Aizerman Conjecture. The Popov Method. Readership: Applied mathematicians and mechanical engineers.



Mathematical Control Theory

Author : Jerzy Zabczyk

Publisher : Springer Science & Business Media

Page : 276 pages

File Size : 41,36 MB

Release : 2008

Category : Language Arts & Disciplines

ISBN : 9780817647322

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Book Description

In a mathematically precise manner, this book presents a unified introduction to deterministic control theory. It includes material on the realization of both linear and nonlinear systems, impulsive control, and positive linear systems.



Mathematical Control Theory

Author : Eduardo D. Sontag

Publisher : Springer Science & Business Media

Page : 543 pages

File Size : 37,79 MB

Release : 2013-11-21

Category : Mathematics

ISBN : 1461205778

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Book Description

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.



Introduction to Mathematical Control Theory

Author : Stephen Barnett

Publisher : Oxford University Press, USA

Page : 424 pages

File Size : 37,51 MB

Release : 1985

Category : Language Arts & Disciplines

ISBN :

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Book Description

In this new edition of a successful text, Professor Barnett, now joined in the authorship by Dr. Cameron, has concentrated on adding material where topics have developed since the first edition, and they have also taken advantage of the extensive classroom testing that has been possible in the intervening years. The book remains the concise readable account of some basic mathematical aspects of control, concentrating on state-space methods and emphasizing points of mathematical interest. As far as the additional material is concerned, the new chapter on multivariable theory reflects some of the significant developments in that field during the past decade, and there is also now an appendix on Kalman filtering. All references have been updated and a large number of new problems for student use have been incorporated.



Mathematical Introduction To Control Theory, A (Second Edition)

Author : Shlomo Engelberg

Publisher : World Scientific Publishing Company

Page : 454 pages

File Size : 36,83 MB

Release : 2015-04-08

Category : Technology & Engineering

ISBN : 178326781X

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Book Description

Striking a nice balance between mathematical rigor and engineering-oriented applications, this second edition covers the bedrock parts of classical control theory — the Routh-Hurwitz theorem and applications, Nyquist diagrams, Bode plots, root locus plots, and the design of controllers (phase-lag, phase-lead, lag-lead, and PID). It also covers three more advanced topics — non-linear control, modern control, and discrete-time control.This invaluable book makes effective use of MATLAB® as a tool in design and analysis. Containing 75 solved problems and 200 figures, this edition will be useful for junior and senior level university students in engineering who have a good knowledge of complex variables and linear algebra.



Control Theory from the Geometric Viewpoint

Author : Andrei A. Agrachev

Publisher : Springer Science & Business Media

Page : 440 pages

File Size : 16,52 MB

Release : 2004-04-15

Category : Language Arts & Disciplines

ISBN : 9783540210191

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Book Description

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 Theory

Author : Velimir Jurdjevic

Publisher : Cambridge University Press

Page : 516 pages

File Size : 21,32 MB

Release : 1997

Category : Mathematics

ISBN : 0521495024

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Book Description

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.



Recent Advances in Differential Equations and Control Theory

Author : Concepción Muriel

Publisher : Springer Nature

Page : 102 pages

File Size : 44,8 MB

Release : 2021-03-13

Category : Mathematics

ISBN : 3030618757

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Book Description

This book collects the latest results and new trends in the application of mathematics to some problems in control theory, numerical simulation and differential equations. The work comprises the main results presented at a thematic minisymposium, part of the 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), held in Valencia, Spain, from 15 to 18 July 2019. The topics covered in the 6 peer-review contributions involve applications of numerical methods to real problems in oceanography and naval engineering, as well as relevant results on switching control techniques, which can have multiple applications in industrial complexes, electromechanical machines, biological systems, etc. Problems in control theory, as in most engineering problems, are modeled by differential equations, for which standard solving procedures may be insufficient. The book also includes recent geometric and analytical methods for the search of exact solutions for differential equations, which serve as essential tools for analyzing problems in many scientific disciplines.



Control Theory and Optimization I

Author : M.I. Zelikin

Publisher : Springer Science & Business Media

Page : 296 pages

File Size : 37,20 MB

Release : 2013-03-14

Category : Mathematics

ISBN : 3662041367

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Book Description

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.