Author: Paul Van Dooren
Publisher: Springer Science & Business Media
ISBN: 1461384192
Category : Mathematics
Languages : en
Pages : 203
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Book Description
During the past decade the interaction between control theory and linear algebra has been ever increasing, giving rise to new results in both areas. As a natural outflow of this research, this book presents information on this interdisciplinary area. The cross-fertilization between control and linear algebra can be found in subfields such as Numerical Linear Algebra, Canonical Forms, Ring-theoretic Methods, Matrix Theory, and Robust Control. This book's editors were challenged to present the latest results in these areas and to find points of common interest. This volume reflects very nicely the interaction: the range of topics seems very wide indeed, but the basic problems and techniques are always closely connected. And the common denominator in all of this is, of course, linear algebra. This book is suitable for both mathematicians and students.
Author: Peter Falb
Publisher: Springer
ISBN: 3319980262
Category : Mathematics
Languages : en
Pages : 211
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Book Description
"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: Frederick Walker Fairman
Publisher: John Wiley & Sons
ISBN: 9780471974895
Category : Science
Languages : en
Pages : 338
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Book Description
Incorporating recent developments in control and systems research,Linear Control Theory provides the fundamental theoreticalbackground needed to fully exploit control system design software.This logically-structured text opens with a detailed treatment ofthe relevant aspects of the state space analysis of linear systems.End-of-chapter problems facilitate the learning process byencouraging the student to put his or her skills into practice.Features include: * The use of an easy to understand matrix variational technique todevelop the time-invariant quadratic and LQG controllers * A step-by-step introduction to essential mathematical ideas asthey are needed, motivating the reader to venture beyond basicconcepts * The examination of linear system theory as it relates to controltheory * The use of the PBH test to characterize eigenvalues in the statefeedback and observer problems rather than its usual role as a testfor controllability or observability * The development of model reduction via balanced realization * The employment of the L2 gain as a basis for the development ofthe H??? controller for the design of controllers in the presenceof plant model uncertainty Senior undergraduate and postgraduate control engineering studentsand practicing control engineers will appreciate the insight thisself-contained book offers into the intelligent use of today scontrol system software tools.
Author: Eduardo D. Sontag
Publisher: Springer Science & Business Media
ISBN: 1461205778
Category : Mathematics
Languages : en
Pages : 543
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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.
Author: Rafael Martínez-Guerra
Publisher: Springer
ISBN: 3030120252
Category : Technology & Engineering
Languages : en
Pages : 201
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Book Description
This book is a short primer in engineering mathematics with a view on applications in nonlinear control theory. In particular, it introduces some elementary concepts of commutative algebra and algebraic geometry which offer a set of tools quite different from the traditional approaches to the subject matter. This text begins with the study of elementary set and map theory. Chapters 2 and 3 on group theory and rings, respectively, are included because of their important relation to linear algebra, the group of invertible linear maps (or matrices) and the ring of linear maps of a vector space. Homomorphisms and Ideals are dealt with as well at this stage. Chapter 4 is devoted to the theory of matrices and systems of linear equations. Chapter 5 gives some information on permutations, determinants and the inverse of a matrix. Chapter 6 tackles vector spaces over a field, Chapter 7 treats linear maps resp. linear transformations, and in addition the application in linear control theory of some abstract theorems such as the concept of a kernel, the image and dimension of vector spaces are illustrated. Chapter 8 considers the diagonalization of a matrix and their canonical forms. Chapter 9 provides a brief introduction to elementary methods for solving differential equations and, finally, in Chapter 10, nonlinear control theory is introduced from the point of view of differential algebra.
Author: Harry L. Trentelman
Publisher: Springer Science & Business Media
ISBN: 1447103394
Category : Technology & Engineering
Languages : en
Pages : 393
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Book Description
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.
Author: Biswa Datta
Publisher: Elsevier
ISBN: 008053788X
Category : Mathematics
Languages : en
Pages : 736
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Book Description
Numerical Methods for Linear Control Systems Design and Analysis is an interdisciplinary textbook aimed at systematic descriptions and implementations of numerically-viable algorithms based on well-established, efficient and stable modern numerical linear techniques for mathematical problems arising in the design and analysis of linear control systems both for the first- and second-order models. - Unique coverage of modern mathematical concepts such as parallel computations, second-order systems, and large-scale solutions - Background material in linear algebra, numerical linear algebra, and control theory included in text - Step-by-step explanations of the algorithms and examples
Author: Jerzy Zabczyk
Publisher: Springer Science & Business Media
ISBN: 9780817647322
Category : Language Arts & Disciplines
Languages : en
Pages : 276
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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.
Author: Andrei A. Agrachev
Publisher: Springer Science & Business Media
ISBN: 3662064049
Category : Science
Languages : en
Pages : 415
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Book Description
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: João P. Hespanha
Publisher: Princeton University Press
ISBN: 0691179573
Category : Mathematics
Languages : en
Pages : 352
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Book Description
A fully updated textbook on linear systems theory Linear systems theory is the cornerstone of control theory and a well-established discipline that focuses on linear differential equations from the perspective of control and estimation. This updated second edition of Linear Systems Theory covers the subject's key topics in a unique lecture-style format, making the book easy to use for instructors and students. João Hespanha looks at system representation, stability, controllability and state feedback, observability and state estimation, and realization theory. He provides the background for advanced modern control design techniques and feedback linearization and examines advanced foundational topics, such as multivariable poles and zeros and LQG/LQR. The textbook presents only the most essential mathematical derivations and places comments, discussion, and terminology in sidebars so that readers can follow the core material easily and without distraction. Annotated proofs with sidebars explain the techniques of proof construction, including contradiction, contraposition, cycles of implications to prove equivalence, and the difference between necessity and sufficiency. Annotated theoretical developments also use sidebars to discuss relevant commands available in MATLAB, allowing students to understand these tools. This second edition contains a large number of new practice exercises with solutions. Based on typical problems, these exercises guide students to succinct and precise answers, helping to clarify issues and consolidate knowledge. The book's balanced chapters can each be covered in approximately two hours of lecture time, simplifying course planning and student review. Easy-to-use textbook in unique lecture-style format Sidebars explain topics in further detail Annotated proofs and discussions of MATLAB commands Balanced chapters can each be taught in two hours of course lecture New practice exercises with solutions included
