Advances in Synchronization of Coupled Fractional Order Systems

Description

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. Front Matter ....Pages i-xix Introduction (Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho)....Pages 1-10 Basic Concepts and Preliminaries (Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho)....Pages 11-39 Synchronization of Chaotic Systems by Means of a Nonlinear Observer: An Application to Secure Communications (Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho)....Pages 41-49 Synchronization for Chaotic System Through an Observer Using the Immersion and Invariance (I&I) Approach (Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho)....Pages 51-60 Synchronization of Nonlinear Fractional-Order Systems by Means of PI\(^{r\alpha }\) Reduced Order Observer (Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho)....Pages 61-70 Estimators for a Class of Commensurate Fractional-Order Systems with Caputo Derivative (Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho)....Pages 71-83 Generalized Multi-synchronization of Fractional Order Liouvillian Chaotic Systems Using Fractional Dynamical Controller (Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho)....Pages 85-130 An Observer for a Class of Incommensurate Fractional Order Systems (Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho)....Pages 131-144 Fractional Generalized Quasi-synchronization of Incommensurate Fractional Order Oscillators (Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho)....Pages 145-159 Synchronization and Anti-synchronization of Fractional Order Chaotic Systems by Means of a Fractional Integral Observer (Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho)....Pages 161-175 Back Matter ....Pages 177-185