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© 2019

Algebraic and Differential Methods for Nonlinear Control Theory

Elements of Commutative Algebra and Algebraic Geometry

Benefits

  • Self-contained and concise primer

  • Geared towards applications in nonlinear control theory

  • Emphasizes tools from ?commutative algebra and algebraic geometry

Book
  • 4.9k Downloads

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 1-17
  3. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 19-30
  4. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 31-47
  5. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 49-64
  6. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 65-73
  7. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 75-91
  8. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 93-107
  9. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 109-123
  10. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 125-161
  11. Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García
    Pages 163-182
  12. Back Matter
    Pages 183-196

About this book

Introduction

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.

Keywords

Fault Detection and Diagnosis in Nonlinear Systems Differential Algebra for Nonlinear Control Theory Synchronization of Coupled Fractional Order Systems Theory of nonlinear control Algebraic structures for engineering mathematics

Authors and affiliations

  1. 1.Departamento de Control AutomáticoCINVESTAV-IPNMexico CityMexico
  2. 2.Departamento de Control AutomáticoCINVESTAV-IPNMexico CityMexico
  3. 3.Departamento de Control AutomáticoCINVESTAV-IPNMexico CityMexico

Bibliographic information

  • Book Title Algebraic and Differential Methods for Nonlinear Control Theory
  • Book Subtitle Elements of Commutative Algebra and Algebraic Geometry
  • Authors Rafael Martínez-Guerra
    Oscar Martínez-Fuentes
    Juan Javier Montesinos-García
  • Series Title Mathematical and Analytical Techniques with Applications to Engineering
  • Series Abbreviated Title Mathematical,Analytical Techniques
  • DOI https://doi.org/10.1007/978-3-030-12025-2
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-3-030-12024-5
  • Softcover ISBN 978-3-030-12027-6
  • eBook ISBN 978-3-030-12025-2
  • Series ISSN 1559-7458
  • Series E-ISSN 1559-7466
  • Edition Number 1
  • Number of Pages XIV, 196
  • Number of Illustrations 2 b/w illustrations, 11 illustrations in colour
  • Topics Engineering Mathematics
    Applications of Nonlinear Dynamics and Chaos Theory
    Control and Systems Theory
    Systems Theory, Control
  • Buy this book on publisher's site
Industry Sectors
Engineering

Reviews

“The book is an introduction to the mathematical tools of control theory, and specifically the differential algebraic approach, for readers with no previous background in this field.” (Filippo Cacace, Mathematical Reviews, October, 2019)