Robust Synchronization of Chaotic Systems via Feedback (Lecture Notes in Control and Information Sciences, 378)

✍ Scribed by Ricardo Femat

• Publisher: Springer
• Year: 2008
• Tongue: English
• Leaves: 205
• Category: Library

✦ Synopsis

This pages include the results derived during last ten years about both suppression and synchronization of chaotic -continuous time- systems. Along this time, our concept was to study how the intrinsic properties of dynamical systems can be exploited to suppress and to synchronize the chaotic behavior and what synchronization phen- ena can be found under feedback interconnection. Our findings have caused surprise to us and have stimulated our astonishing capability. Perhaps, reader can imagine our faces with opens eyes like children seeing around objects; which are possibly obvious for others and novel for us. A compilation of our surprises about these findings is being described along this book. Book contains both objectives to share our ama- ment and to show our perspective on synchronization of chaotic systems. Thus, while we were writing the preface, we discussed its scope. Thinking as a book readers, we found that a preface should answer, in few words, the following question: What can the reader find in this book?, reader can find our steps toward understanding of c- otic behavior and the possibility of suppressing and synchronizing it. We firstly show the chaos suppression form experimental domain to potential implementation in high tech system as a levitation system based on High Temperature Superconductors (HTS). This chapter is used as departing point towards a more complicated problem the chaotic synchronization. Then, reader travels by the synchronization of the chaotic behavior world throughout distinct feedback approaches.

✦ Table of Contents

Title Page
Preface
Contents
Introduction to Chaos Control: An Interdisciplinary Problem
Chaos Control Is Suppression or Synchronization
References
Chaos Suppression with Least Prior Knowledge: Continuous Time Feedback
Experimental Space in Frequency Domain
Laplace Domain Controllers for Chaos Suppression
The PI Controller
A Design Procedure for Laplace Domain Controllers with Dynamic Estimation
Rationale of Chaos Stabilization Via Robust Geometrical Control
Suppressing Chaos in Second-Order Systems
Sketching the Stability Analysis
The Force between HTS Surface and the Levitated Magnet
Summary
References
Robust Synchronization of Chaotic Systems: A Proportional Integral Approach
Chaos Synchronization Via Linear Feedback
The Feedback Control Scheme
The Chaos Synchronization as a Stabilization Problem
A PI Controller with Uncertainties Estimation
Local Stability Analysis for an Illustrative Example
Numerical Results for a Synchronization System
The Performance Index and Tuning Procedure
Chaos Synchronization Phenomena: A Classification
Some Synchronization Phenomena
Chaos-Based Signal Transmission Despite Master/Slave Mismatches: An Experimental Test
The Chaos-Based Scheme
Experimental Setup
Robust Stability Analysis of Chaos Synchronization
Chaos Synchronization Via Linear Feedback
Robust Stability Analysis of Synchronization Error
Illustrative Example
References
Robust Synchronization Via Geometrical Control: A General Framework
Synchronization of Second-Order Driven Systems with Different Model
Problem Statement
Synchronization Despite Unknown Master Model
Numerical Simulations
Adaptive Synchronization of High-Order Chaotic Systems: A Feedback with Low Order Parameterization
Preliminaries
Synchronization against Uncertain Vector Fields
Complete Practical Synchronization of Chaotic Systems
Synchronization of an Inhomogeneous Chain of Oscillators
Chaos-Based Communication Scheme Via Robust Asymptotic Feedback
Problem Statement
Results on Secure Communication Via Feedback
Illustrative Examples
References
Discrete-Time Feedback for Chaos Control and Synchronization
Discrete - Time Control of Systems with Friction
Position Regulation of a Friction System
The Friction Force and Its Complexity
The Irregular Behavior of the Friction System
Stabilization of the Friction System
Chaos Suppression Via a Discrete-Time Controller
Chaos Control of the Second-Order Driven Oscillators
The Feedback Control without Velocity Measurements
The Discrete-Time Feedback Via Uncertainties Estimation
Numerical Simulations and Representative Examples
Discussion about the Chaos Control
Discrete-Time Chaos Control and Its Implications
A Robust Recursive Feedback Law
Synchronization of Chaotic Systems with Different Order
Problem Statement
The Proposed Feedback and Design Details
Reduced-Order Synchronization under Partial Knowledge
Reduced-Order Synchronization with Least Prior Knowledge
Discussion of the Results
References
Remarks on Chaos Synchronizability and Synchronization
Complete Synchronizability
The Chaos Synchronization Problem
Synchronizability from Control of Chaotic Systems
Complete Synchronizability of Chaotic Systems
Illustrative Example
General Framework of Chaotic Synchronization Based on Lie Algebra
Lie-Based Geometry of Nonlinear Systems
Involutive Distributions and Flows
Computing the Synchronization Function
References
Index
Abbreviations