STABILIZATION OF CHAOTIC SYSTEMS USING LINEAR SAMPLED-DATA CONTROLLER

2007 ◽  
Vol 17 (06) ◽  
pp. 2021-2031 ◽  
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.

scholarly journals Aperiodic Sampled-Data Control for Chaotic System Based on Takagi–Sugeno Fuzzy Model

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Minjie Zheng ◽  
Shenhua Yang ◽  
Lina Li
Keyword(s):  
Chaotic System ◽  
Fuzzy Model ◽  
Sampling Period ◽  
Linear Matrix ◽  
Sampled Data ◽  
Data Control ◽  
Sampled Data Control ◽  
Mean Square Exponential Stability ◽  
Data Controller ◽  
Takagi Sugeno

This paper investigates the aperiodic sampled-data control for a chaotic system. Firstly, Takagi–Sugeno (T-S) fuzzy models for the chaotic systems are established. The lower and upper bounds of the sampling period are taken into consideration. Then, the criteria for mean square exponential stability analysis and aperiodic sampled-data controller synthesis are provided by means of linear matrix inequalities. And the real sampling patterns can be fully captured by constructing suitable Lyapunov functions. Finally, an illustrative example shows that the proposed method is effective to guarantee that the system’s states are stable with aperiodic sampled data.

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

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
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.

scholarly journals Control of Chaos Using Sampled-Data Feedback Control

1998 ◽  
Vol 08 (12) ◽  
pp. 2433-2438 ◽  
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.

New globally asymptotical synchronization of chaotic systems under sampled-data controller

2014 ◽  
Vol 78 (4) ◽  
pp. 2409-2419 ◽  
Author(s):  
Chao Ge ◽  
Zhigang Li ◽  
Xiaohong Huang ◽  
Caijuan Shi
Keyword(s):  
Chaotic Systems ◽  
Sampled Data ◽  
Data Controller

scholarly journals Analyses and Encryption Implementation of a New Chaotic System Based on Semitensor Product

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Rui Wang ◽  
Peifeng Du ◽  
Wenqi Zhong ◽  
Han Han ◽  
Hui Sun
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
High Dimensions ◽  
New Chaotic System ◽  
Different Dimensions ◽  
Hardware Encryption ◽  
The Individual ◽  
New System ◽  
Randomness Tests

Semitensor product theory can deal with matrices multiplication with different numbers of columns and rows. Therefore, a new chaotic system for different high dimensions can be created by employing a semitensor product of chaotic systems with different dimensions, so that more channels can be selected for encryption. This paper proposes a new chaotic system generated by semitensor product applied on Qi and Lorenz systems. The corresponding dynamic characteristics of the new system are discussed in this paper to verify the existences of different attractors. The detailed algorithms are illustrated in this paper. The FPGA hardware encryption implementations are also elaborated and conducted. Correspondingly, the randomness tests are realized as well, and compared to that of the individual Qi system and Lorenz system, the proposed system in this paper owns the better randomness characteristic. The statistical analyses and differential and correlation analyses are also discussed.

SYNCHRONIZATION OF TWO UNCERTAIN CHAOTIC SYSTEMS VIA ADAPTIVE BACKSTEPPING

2001 ◽  
Vol 11 (06) ◽  
pp. 1743-1751 ◽  
Author(s):  
C. WANG ◽  
S. S. GE
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Design Procedure ◽  
Research Literature ◽  
Adaptive Synchronization ◽  
Adaptive Backstepping ◽  
Feedback Form ◽  
Bounded Linear ◽  
Nonlinear Chaotic System ◽  
Uncertain Chaotic Systems

In this letter, adaptive synchronization of two uncertain chaotic systems is presented using adaptive backstepping with tuning functions. The master system is any smooth, bounded, linear-in-the-parameters nonlinear chaotic system, while the slave system is a nonlinear chaotic system in the strict-feedback form. Both master and slave systems are with key parameters unknown. Global stability and asymptotic synchronization between the outputs of master and slave systems can be achieved. The proposed approach offers a systematic design procedure for adaptive synchronization of a large class of continuous-time chaotic systems in the chaos research literature. Simulation results are presented to show the effectiveness of the approach.

Generating the New Chaotic Attractors of the Lorenz System Family via Anti-Controlling Method

2012 ◽  
Vol 542-543 ◽  
pp. 1042-1046 ◽  
Author(s):  
Xin Deng
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Attractors ◽  
Chen System ◽  
Lü System ◽  
New Chaotic System ◽  
Dynamical Properties ◽  
The Lorenz System ◽  
Lu System

In this paper, the first new chaotic system is gained by anti-controlling Chen system,which belongs to the general Lorenz system; also, the second new chaotic system is gained by anti-controlling the first new chaotic system, which belongs to the general Lü system. Moreover,some basic dynamical properties of two new chaotic systems are studied, either numerically or analytically. The obtained results show clearly that Chen chaotic system and two new chaotic systems also can form another Lorenz system family and deserve further detailed investigation.

scholarly journals Symmetry Evolution in Chaotic System

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 574 ◽  
Author(s):  
Chunbiao Li ◽  
Jiayu Sun ◽  
Tianai Lu ◽  
Tengfei Lei
Keyword(s):  
Dynamical System ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
System Transformation ◽  
Conditional Symmetry ◽  
Offset Boosting ◽  
Key Factor

A comprehensive exploration of symmetry and conditional symmetry is made from the evolution of symmetry. Unlike other chaotic systems of conditional symmetry, in this work it is derived from the symmetric diffusionless Lorenz system. Transformation from symmetry and asymmetry to conditional symmetry is examined by constant planting and dimension growth, which proves that the offset boosting of some necessary variables is the key factor for reestablishing polarity balance in a dynamical system.

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