Synchronization of Chaotic Systems Using Sampled-Data Polynomial Controller

This paper presents the synchronization of two chaotic systems, namely the drive and response chaotic systems, using sampled-data polynomial controllers. The sampled-data polynomial controller is employed to drive the system states of the response chaotic system to follow those of the drive chaotic system. Because of the zero-order-hold unit complicating the system dynamics by introducing discontinuity to the system, it makes the stability analysis difficult. However, the sampled-data polynomial controller can be readily implemented by a digital computer or microcontroller to lower the implementation cost and time. With the sum-of-squares (SOS) approach, the system to be handled can be in the form of nonlinear state-space equations with the system matrix depending on system states. Based on the Lyapunov stability theory, SOS-based stability conditions are obtained to guarantee the system stability and realize the chaotic synchronization subject to an H∞ performance function. The solution to the SOS-based stability conditions can be found numerically using the third-party Matlab toolbox SOSTOOLS. Simulation examples are given to illustrate the merits of the proposed sampled-data polynomial control approach for chaotic synchronization problems.

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SYNCHRONIZATION OF CHAOTIC SYSTEMS USING NEURAL-NETWORK-BASED CONTROLLER

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127407018269 ◽

2007 ◽

Vol 17 (06) ◽

pp. 2117-2125 ◽

Cited By ~ 9

Author(s):

H. K. LAM ◽

L. D. SENEVIRATNE

Keyword(s):

Neural Network ◽

Neural Networks ◽

System Performance ◽

Chaotic Systems ◽

Chaotic Synchronization ◽

System Stability ◽

Stability Conditions ◽

Feed Forward Neural Network ◽

Generalized Eigenvalue ◽

The Neural Networks

This paper presents the synchronization of chaotic systems. A feed-forward neural network will be employed to form the proposed neural-network-based controller to perform chaotic synchronization. Stability conditions will be derived to guarantee the system stability. The system performance will be ensured and the parameters of the neural networks can be obtained by solving the solution to the generalized eigenvalue minimization problem. A simulation example will be given to illustrate the effectiveness of the proposed approach.

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STABILIZATION OF CHAOTIC SYSTEMS USING LINEAR SAMPLED-DATA CONTROLLER

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127407018191 ◽

2007 ◽

Vol 17 (06) ◽

pp. 2021-2031 ◽

Cited By ~ 20

Author(s):

H. K. LAM ◽

F. H. F. LEUNG

Keyword(s):

Chaotic System ◽

Chaotic Systems ◽

Lorenz System ◽

Design Procedure ◽

Sampling Period ◽

Feedback Gain ◽

Sampled Data ◽

Lyapunov Approach ◽

And Performance ◽

Data Controller

This paper proposes a linear sampled-data controller for the stabilization of chaotic system. The system stabilization and performance issues will be investigated. Stability conditions will be derived based on the Lyapunov approach. The findings of the maximum sampling period and the feedback gain of controller, and the optimization of system performance will be formulated as a generalized eigenvalue minimization problem. Based on the analysis result, a stable linear sampled-data controller can be realized systematically to stabilize a chaotic system. An example of stabilizing a Lorenz system will be given to illustrate the design procedure and effectiveness of the proposed approach.

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The Model of Liu Chaotic Synchronization with Oscillating Parameters under the Impulsive Control

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.480-481.1378 ◽

2011 ◽

Vol 480-481 ◽

pp. 1378-1382

Author(s):

Yan Hui Chen

Keyword(s):

Chaotic System ◽

Secure Communication ◽

Chaotic Systems ◽

Impulsive Control ◽

Impulsive Differential Equations ◽

Chaotic Synchronization ◽

Control Signal ◽

Synchronization Control ◽

Security Risks ◽

Control Scheme

The control of chaotic synchronization is the kernel technology in chaos-based secure communication. Those control methods have to transmitting control signal which increase the security risks of the communication system. Attacker can reconstruct the chaotic system or estimate parameters by using the information of the chaotic system. In this paper we propose a hybrid Liu chaotic synchronization control scheme which contains both continuous chaotic system with oscillating parameters approach to 0 and discrete chaotic system. By theory of impulsive differential equations, we proved a theorem that two continuous Liu chaotic systems can get synchronized without control signal transmitting which has reduced the risk of the security.

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Control of Chaos Using Sampled-Data Feedback Control

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127498001947 ◽

1998 ◽

Vol 08 (12) ◽

pp. 2433-2438 ◽

Cited By ~ 24

Author(s):

Tao Yang

Keyword(s):

Feedback Control ◽

Asymptotic Stability ◽

Chaotic System ◽

Chaotic Systems ◽

Sampling Rate ◽

Control Input ◽

Sampled Data ◽

Control Of Chaos ◽

Data Feedback ◽

Theoretical Results

In this paper we present a theory for control of chaotic systems using sampled data. The output of the chaotic system is sampled at a given sampling rate and the sampled output is used by a feedback subsystem to construct a control signal, which is held constant by a holding subsystem. Hence, during each control iteration, the control input remains unchanged. Theoretical results on the asymptotic stability of the resulting controlled chaotic systems are presented. Numerical experimental results via Chua's circuit are used to verify the theoretical results.

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Chaotic Synchronization of a Class of Nonlinear Systems via Sampled-Data State Feedback

Volume 3: Industrial Applications; Modeling for Oil and Gas, Control and Validation, Estimation, and Control of Automotive Systems; Multi-Agent and Networked Systems; Control System Design; Physical Human-Robot Interaction; Rehabilitation Robotics; Sensing and Actuation for Control; Biomedical Systems; Time Delay Systems and Stability; Unmanned Ground and Surface Robotics; Vehicle Motion Controls; Vibration Analysis and Isolation; Vibration and Control for Energy Harvesting; Wind Energy ◽

10.1115/dscc2014-5991 ◽

2014 ◽

Author(s):

Song Yan ◽

Chunjiang Qian ◽

Tingwen Huang

Keyword(s):

Chaotic System ◽

State Feedback ◽

Tracking Error ◽

Practical Importance ◽

Sampled Data ◽

Data Feedback ◽

Sampled Signal ◽

System States ◽

Data Controller ◽

Chua Oscillator

This paper presents a control strategy for the problem of using sampled-data feedback to synchronize a slave chaotic system with a master chaotic system. The problem is of practical importance since in practice the system states is transmitted as a sampled signal. In order to solve this problem, a sampled-data controller using state feedback is designed to make the tracking error converge to zero. An application to a chaotic Chua oscillator illustrates the effectiveness of the proposed approach.

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Sliding observer for synchronization of fractional order chaotic systems with mismatched parameter

Open Physics ◽

10.2478/s11534-012-0073-4 ◽

2012 ◽

Vol 10 (5) ◽

Cited By ~ 8

Author(s):

Hadi Delavari ◽

Danial Senejohnny ◽

Dumitru Baleanu

Keyword(s):

Lyapunov Function ◽

Fractional Order ◽

Canonical Form ◽

Chaotic System ◽

Finite Time ◽

Chaotic Systems ◽

Sliding Mode ◽

Chaotic Synchronization ◽

Mode Theory ◽

Synchronization Scheme

AbstractIn this paper, we propose an observer-based fractional order chaotic synchronization scheme. Our method concerns fractional order chaotic systems in Brunovsky canonical form. Using sliding mode theory, we achieve synchronization of fractional order response with fractional order drive system using a classical Lyapunov function, and also by fractional order differentiation and integration, i.e. differintegration formulas, state synchronization proved to be established in a finite time. To demonstrate the efficiency of the proposed scheme, fractional order version of a well-known chaotic system; Arnodo-Coullet system is considered as illustrative examples.

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The Synchronization of Super-Chen Chaotic Scheme with a Sort of Oscillating Parameters

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.282-283.612 ◽

2011 ◽

Vol 282-283 ◽

pp. 612-615

Author(s):

Ying Kui Li

Keyword(s):

Chaotic System ◽

Secure Communication ◽

Chaotic Systems ◽

Chaotic Synchronization ◽

Control Signal ◽

Synchronization Control ◽

Two Systems ◽

Control And Synchronization ◽

Synchronization Scheme

Most properties of Super Chen’s chaotic system satisfy with the requirements of secure communication and cryptography. Implusive stabilzation for control and synchronization of Super Chen’s chaotic systems can be applied in secure communication. Super Chen’s Chaotic synchronization control can be the kernel technology in chaos-based secure commu-nication. In this paper we propose a hybrid Super Chen chaotic synchronization scheme control which contains both continuous chaotic system with a sort of oscillating parameters and discrete chaotic system. If oscillating parameters approach to 0, we proved that two systems can get synchronized without control signal transmitting.

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Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127419501979 ◽

2019 ◽

Vol 29 (14) ◽

pp. 1950197 ◽

Cited By ~ 2

Author(s):

P. D. Kamdem Kuate ◽

Qiang Lai ◽

Hilaire Fotsin

Keyword(s):

Chaotic System ◽

Chaotic Systems ◽

Lorenz System ◽

Chaotic Behavior ◽

Piecewise Linear ◽

Period Doubling ◽

Adaptive Synchronization ◽

The Novel ◽

Algebraic Equations ◽

The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

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Complex dynamical behaviors of a novel exponential hyper–chaotic system and its application in fast synchronization and color image encryption

Science Progress ◽

10.1177/00368504211003388 ◽

2021 ◽

Vol 104 (1) ◽

pp. 003685042110033

Author(s):

Javad Mostafaee ◽

Saleh Mobayen ◽

Behrouz Vaseghi ◽

Mohammad Vahedi ◽

Afef Fekih

Keyword(s):

Image Encryption ◽

Chaotic System ◽

Sliding Mode ◽

Color Image ◽

Equilibrium Points ◽

Lyapunov Stability Theory ◽

System Stability ◽

Color Image Encryption ◽

Terminal Sliding Mode ◽

Finite Time Stability

This paper proposes a novel exponential hyper–chaotic system with complex dynamic behaviors. It also analyzes the chaotic attractor, bifurcation diagram, equilibrium points, Poincare map, Kaplan–Yorke dimension, and Lyapunov exponent behaviors. A fast terminal sliding mode control scheme is then designed to ensure the fast synchronization and stability of the new exponential hyper–chaotic system. Stability analysis was performed using the Lyapunov stability theory. One of the main features of the proposed controller is the finite time stability of the terminal sliding surface designed with high–order power function of error and derivative of error. The approach was implemented for image cryptosystem. Color image encryption was carried out to confirm the performance of the new hyper–chaotic system. For image encryption, the DNA encryption-based RGB algorithm was used. Performance assessment of the proposed approach confirmed the ability of the proposed hyper–chaotic system to increase the security of image encryption.

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