This book provides a general overview of several concepts of synchronization and brings together related approaches to secure communication in chaotic systems. This is achieved using a combination of analytic, algebraic, geometrical and asymptotical methods to tackle the dynamical feedback stabilization problem. In particular, differential-geometric and algebraic differential concepts reveal important structural properties of chaotic systems and serve as guide for the construction of design procedures for a wide variety of chaotic systems. The basic differential algebraic and geometric concepts are presented in the first few chapters in a novel way as design tools, together with selected experimental studies demonstrating their importance. The subsequent chapters treat recent applications. Written for graduate students in applied physical sciences, systems engineers, and applied mathematicians interested in synchronization of chaotic systems and in secure communications, this self-contained text requires only basic knowledge of integer ordinary and fractional ordinary differential equations. Design applications are illustrated with the help of several physical models of practical interest.
Author(s): Rafael Martínez-Guerra, Claudia A. Pérez-Pinacho, Gian Carlo Gómez-Cortés (auth.)
Series: Understanding Complex Systems
Edition: 1
Publisher: Springer International Publishing
Year: 2015
Language: English
Pages: 242
Tags: Nonlinear Dynamics; Vibration, Dynamical Systems, Control; Classical Continuum Physics; Complexity
Front Matter....Pages i-xxiv
Control Theory and Synchronization....Pages 1-31
A Model-free Model-Free-Based Proportional Reduced-order observer Reduced-Order Observer Design for the Synchronization of Lorenz system Lorenz Systems....Pages 33-42
A Model-Free Sliding Observer to the Synchronization Problem Using Geometric Techniques....Pages 43-62
Experimental synchronization Experimental Synchronization by Means of Observers....Pages 63-100
Synchronization of an Uncertain Rikitake System with Parametric Estimation....Pages 101-110
Secure Communications and Synchronization via a Sliding-Mode Observer....Pages 111-124
Synchronization and Antisynchronization of Chaotic Systems: A Differential and Algebraic Approach....Pages 125-133
Synchronization of Chaotic Liouvillian Systems: An Application to Chua’s Oscillator....Pages 135-151
Synchronization of Partially Unknown Nonlinear Fractional-Order Systems....Pages 153-162
Generalized Synchronization via the Differential Primitive Element....Pages 163-174
Generalized Synchronization for a Class of Nondifferentially Flat and Liouvillian Chaotic Systems....Pages 175-186
Generalized Multisynchronization by Means of a Family of Dynamical Feedbacks....Pages 187-202
Fractional Generalized Synchronization in Nonlinear Fractional-Order Systems via Dynamical Feedback....Pages 203-218
An Observer for a Class of Incommensurate Fractional-Order Systems....Pages 219-236
Back Matter....Pages 237-242
