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Advances in Synchronization of Coupled Fractional Order Systems

Fundamentals and Methods

  • Rafael Martínez-Guerra
  • Claudia Alejandra Pérez-Pinacho

Part of the Understanding Complex Systems book series (UCS)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho
    Pages 1-10
  3. Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho
    Pages 11-39
  4. Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho
    Pages 41-49
  5. Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho
    Pages 51-60
  6. Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho
    Pages 61-70
  7. Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho
    Pages 71-83
  8. Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho
    Pages 131-144
  9. Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho
    Pages 145-159
  10. Back Matter
    Pages 177-185

About this book

Introduction

After a short introduction to the fundamentals, this book provides a detailed account of major advances in applying fractional calculus to dynamical systems. Fractional order dynamical systems currently continue to gain further importance in many areas of science and engineering.

 

As with many other approaches to mathematical modeling, the first issue to be addressed is the need to couple a definition of the fractional differentiation or integration operator with the types of dynamical systems that are analyzed. As such, for the fundamentals the focus is on basic aspects of fractional calculus, in particular stability analysis, which is required to tackle synchronization in coupled fractional order systems, to understand the essence of estimators for related integer order systems, and to keep track of the interplay between synchronization and parameter observation. This serves as the common basis for the more advanced topics and applications presented in the subsequent chapters, which include an introduction to the 'Immersion and Invariance' (I&I) methodology, the masterslave synchronization scheme for partially known nonlinear fractional order systems, Fractional Algebraic Observability (FAO) and Fractional Generalized quasi-Synchronization (FGqS) to name but a few.

 

This book is intended not only for applied mathematicians and theoretical physicists, but also for anyone in applied science dealing with complex nonlinear systems. 


Keywords

Fractional Calculus Generalized Synchronization Fractional Order Estimators Immersion and Invariance Methodology Fractional Dynamical Controllers fractional order dynamical systems fractional order systems modeling secure communications Master–slave synchronization

Authors and affiliations

  • Rafael Martínez-Guerra
    • 1
  • Claudia Alejandra Pérez-Pinacho
    • 2
  1. 1.Automatic ControlCINVESTAV-IPNMexico CityMexico
  2. 2.Automatic ControlCINVESTAV-IPNMexico CityMexico

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-93946-9
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-93945-2
  • Online ISBN 978-3-319-93946-9
  • Series Print ISSN 1860-0832
  • Series Online ISSN 1860-0840
  • Buy this book on publisher's site