ON ADAPTIVE SYNCHRONIZATION AND CONTROL OF NONLINEAR DYNAMICAL SYSTEMS

1996 ◽  
Vol 06 (03) ◽  
pp. 455-471 ◽  
Author(s):  
CHAI WAH WU ◽  
TAO YANG ◽  
LEON O. CHUA
Keyword(s):  
Spread Spectrum ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Nonlinear Dynamical Systems ◽  
Adaptive Synchronization ◽  
Adaptive Controllers ◽  
Nonlinear Dynamical ◽  
Two Systems ◽  
And Control

In this paper, we study the synchronization of two coupled nonlinear, in particular chaotic, systems which are not identical. We show how adaptive controllers can be used to adjust the parameters of the systems such that the two systems will synchronize. We use a Lyapunov function approach to prove a global result which shows that our choice of controllers will synchronize the two systems. We show how it is related to Huberman-Lumer adaptive control and the LMS adaptive algorithm. We illustrate the applicability of this method using Chua's oscillators as the chaotic systems. We choose parameters for the two systems which are orders of magnitude apart to illustrate the effectiveness of the adaptive controllers. Finally, we discuss the role of adaptive synchronization in the context of secure and spread spectrum communication systems. In particular, we show how several signals can be encoded onto a single scalar chaotic carrier signal.

scholarly journals AN ADAPTIVE APPROACH TO THE CONTROL AND SYNCHRONIZATION OF CONTINUOUS-TIME CHAOTIC SYSTEMS

1996 ◽  
Vol 06 (03) ◽  
pp. 557-568 ◽  
Author(s):  
MARIO DI BERNARDO
Keyword(s):  
Chaotic Systems ◽  
Nonlinear Dynamical Systems ◽  
Adaptive Estimation ◽  
Lyapunov Theory ◽  
Adaptive Approach ◽  
Nonlinear Dynamical ◽  
Complete Knowledge ◽  
Feedforward Controller ◽  
Control And Synchronization ◽  
And Control

This paper is concerned with synchronization and control of chaotic nonlinear dynamical systems. First, a unified frame for both the synchronization and the control problem is described. Then by modifying a feedback plus feedforward controller, a discontinuous strategy is synthesized which exploits the boundedness of chaotic attractors and limit cycles. Finally, an adaptive approach is investigated and an adaptive estimation law is implemented. The result, which is both global and not reliant on complete knowledge of the systems involved, is rigorously proved by means of Lyapunov Theory. An application to the synchronization of two chaotic systems is presented.

Analisis Karakterisasi Teknologi Direct Sequence Spread Spectrum Dan Frequency Hopping Spread Spectrum

2019 ◽  
Vol 2 (2) ◽  
pp. 129-138
Author(s):  
Fawzan Galib Abdul Karim Bawahab ◽  
Elvan Yuniarti ◽  
Edi Kurniawan
Keyword(s):  
Spread Spectrum ◽  
Communication Systems ◽  
Multiple Access ◽  
Frequency Hopping ◽  
Direct Sequence Spread Spectrum ◽  
Direct Sequence ◽  
Frequency Hopping Spread Spectrum ◽  
Two Systems ◽  
The Difference

Abstrak. Pada penelitian ini, telah dilakukan analisa karakterisasi pada teknologi Direct Sequence Spread Spectrum dan Frequency Hopping Spread Spectrum, sebagai salah satu teknik multiple-access pada sistem komunikasi. Karakterisasi dilakukan untuk mencari bagaimana cara meningkatkan keoptimalan kedua sistem tersebut, dalam mengatasi masalah interferensi dengan sistem dan channel yang sama. Dan juga untuk menentukan veriabel apa yang mempengaruhi keoptimalan kedua sistem tersebut. Karakterisasi dilakukan dengan menentukan variabel-variabel yang mempengaruhi keoptimalan keduanya. Hasil dari karakterisasi, diketahui variabel-variabel yang mempengaruhi kemampuan sistem DSSS yaitu nilai frekuensi spreading (). Sedangkan untuk sistem FHSS yaitu nilai frekuensi spreading ( dan ) dan selisih antara frekuensi hopping data dengan frekuensi hopping interferensi . Kata Kunci: BER, DSSS, FHSS, Interference, Spread spectrum. Abstract. In this study, characterization of Direct Sequence Spread Spectrum and Frequency Hopping Spread Spectrum technologies have been done, as one of the multiple-access techniques in communication systems. Characterization is done to find out how to improve the ability of the two systems, in solving interference problems with the same system and channel. And also to determine what veriabel affects the ability of the two systems. Characterization is done by determining the variables that affect the ability of both. The results of the characterization, known variables that affect the ability of the DSSS system are the spreading frequency value (). As for the FHSS system, the spreading frequency value ( and ) and the difference between frequency hopping data with frequency hopping interference .

Numerical characterization of nonlinear dynamical systems using parallel computing: The role of GPUs approach

2016 ◽  
Vol 37 ◽  
pp. 143-162 ◽  
Author(s):  
Filipe I. Fazanaro ◽  
Diogo C. Soriano ◽  
Ricardo Suyama ◽  
Marconi K. Madrid ◽  
José Raimundo de Oliveira ◽  
...  
Keyword(s):  
Parallel Computing ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Numerical Characterization

scholarly journals Chaos and Control in Coronary Artery System

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yanxiang Shi
Keyword(s):  
Coronary Artery ◽  
Feedback Control ◽  
Numerical Simulations ◽  
Melnikov Method ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Nonlinear Dynamical ◽  
The Road ◽  
Two Systems ◽  
And Control

Two types of coronary artery system N-type and S-type, are investigated. The threshold conditions for the occurrence of Smale horseshoe chaos are obtained by using Melnikov method. Numerical simulations including phase portraits, potential diagram, homoclinic bifurcation curve diagrams, bifurcation diagrams, and Poincaré maps not only prove the correctness of theoretical analysis but also show the interesting bifurcation diagrams and the more new complex dynamical behaviors. Numerical simulations are used to investigate the nonlinear dynamical characteristics and complexity of the two systems, revealing bifurcation forms and the road leading to chaotic motion. Finally the chaotic states of the two systems are effectively controlled by two control methods: variable feedback control and coupled feedback control.

ADAPTIVE SYNCHRONIZATION OF CHAOTIC SYSTEMS VIA STATE OR OUTPUT FEEDBACK CONTROL

2001 ◽  
Vol 11 (04) ◽  
pp. 1149-1158 ◽  
Author(s):  
YIGUANG HONG ◽  
HUASHU QIN ◽  
GUNARONG CHEN
Keyword(s):  
Output Feedback ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Output Feedback Control ◽  
Robust Adaptive Control ◽  
Adaptive Synchronization ◽  
Feedback Controls ◽  
Adaptive Controllers ◽  
Modification Technique ◽  
Robust Adaptive

This letter addresses the problem of robust adaptive control for synchronization of continuous-time coupled chaotic systems, which may be subjected to disturbances. A general model is studied via two different approaches, using either state feedback or measured output feedback controls. Adaptive controllers are designed, in which a sliding mode structure is employed to increase the robustness of the closed-loop systems. When only output variables are measurable for synchronization, the adaptive controllers are designed by incorporating with a filter and using the so-called σ-modification technique. Several numerical examples are presented to show the effectiveness of the proposed chaos synchronization methods.

COMPETITIVE MODES AND THEIR APPLICATION

2006 ◽  
Vol 16 (03) ◽  
pp. 497-522 ◽  
Author(s):  
WEIGUANG YAO ◽  
PEI YU ◽  
CHRISTOPHER ESSEX ◽  
MATT DAVISON
Keyword(s):  
Chaotic Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Point Of View ◽  
Frequency Function ◽  
Mode Competition ◽  
Integration Scheme ◽  
Nonlinear Dynamical ◽  
Competitive Modes ◽  
Definition Of

We investigate nonlinear dynamical systems from the mode competition point of view, and propose the necessary conditions for a system to be chaotic. We conjecture that a chaotic system has at least two competitive modes (CM's). For a general nonlinear dynamical system, we give a simple, dynamically motivated definition of mode suitable for this concept. Since for most chaotic systems it is difficult to obtain the form of a CM, we focus on the competition between the corresponding modulated frequency components of the CM's. Some direct applications result from the explicit form of the frequency functions. One application is to estimate parameter regimes which may lead to chaos. It is shown that chaos may be found by analyzing the frequency function of the CM's without applying a numerical integration scheme. Another application is to create new chaotic systems using custom-designed CM's. Several new chaotic systems are reported.

Sign in / Sign up

Export Citation Format

Share Document