Lecture Notes in Mathematics

Invariance Entropy for Deterministic Control Systems

An Introduction

Authors: Kawan, Christoph

  • The first book to present results on the relatively new notions of feedback and invariance entropy
  • Provides detailed proofs of all key results, together with a comprehensive exposition of the mathematical background material used therein
  • Will be particularly interesting for readers with a background in dynamical systems theory
  • The basic knowledge of control theory needed for its understanding is presented at great length in the first chapter
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  • ISBN 978-3-319-01288-9
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About this book

This monograph provides an introduction to the concept of invariance entropy, the central motivation of which lies in the need to deal with communication constraints in networked control systems. For the simplest possible network topology, consisting of one controller and one dynamical system connected by a digital channel, invariance entropy provides a measure for the smallest data rate above which it is possible to render a given subset of the state space invariant by means of a symbolic coder-controller pair. This concept is essentially equivalent to the notion of topological feedback entropy introduced by Nair, Evans, Mareels and Moran (Topological feedback entropy and nonlinear stabilization. IEEE Trans. Automat. Control 49 (2004), 1585–1597). The book presents the foundations of a theory which aims at finding expressions for invariance entropy in terms of dynamical quantities such as Lyapunov exponents. While both discrete-time and continuous-time systems are treated, the emphasis lies on systems given by differential equations.

Reviews

From the book reviews:

“The topics are well organized, the exposition is clear and there are examples to illustrate the theoretical results. This book is highly recommended for both researchers and graduate students in dynamical systems, control theory and related areas. This book is particularly useful because it collects in one place a large number of seminal results that are essential for an understanding of invariance entropy.” (Alexandre José Santana, Mathematical Reviews, August, 2014)

Table of contents (7 chapters)

  • Basic Properties of Control Systems

    Kawan, Christoph

    Pages 1-42

  • Introduction to Invariance Entropy

    Kawan, Christoph

    Pages 43-87

  • Linear and Bilinear Systems

    Kawan, Christoph

    Pages 89-105

  • General Estimates

    Kawan, Christoph

    Pages 107-120

  • Controllability, Lyapunov Exponents, and Upper Bounds

    Kawan, Christoph

    Pages 121-150

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-319-01288-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA
  • ISBN 978-3-319-01287-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Invariance Entropy for Deterministic Control Systems
Book Subtitle
An Introduction
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2089
Copyright
2013
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-01288-9
DOI
10.1007/978-3-319-01288-9
Softcover ISBN
978-3-319-01287-2
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XXII, 270
Number of Illustrations and Tables
1 b/w illustrations, 1 illustrations in colour
Topics