scholarly journals Chaos Synchronization for Hyperchaotic Lorenz-Type System via Fuzzy-Based Sliding-Mode Observer

2020 ◽  
Vol 25 (1) ◽  
pp. 16
Author(s):  
Corina Plata ◽  
Pablo J. Prieto ◽  
Ramon Ramirez-Villalobos ◽  
Luis N. Coria
Keyword(s):  
Chaos Synchronization ◽  
Sliding Mode ◽  
Type System ◽  
Sliding Mode Observer ◽  
Hyperchaotic System ◽  
Science And Engineering ◽  
Synchronization Problem ◽  
High Frequency Oscillations ◽  
Encryption And Decryption ◽  
Hyperchaotic Systems

Hyperchaotic systems have applications in multiple areas of science and engineering. The study and development of these type of systems helps to solve diverse problems related to encryption and decryption of information. In order to solve the chaos synchronization problem for a hyperchaotic Lorenz-type system, we propose an observer based synchronization under a master-slave configuration. The proposed methodology consists of designing a sliding-mode observer (SMO) for the hyperchaotic system. In contrast, this type of methodology exhibits high-frequency oscillations, commonly known as chattering. To solve this problem, a fuzzy-based SMO system was designed. Numerical simulations illustrate the effectiveness of the synchronization between the hyperchaotic system obtained and the proposed observer.

Synchronizing the Noise-Perturbed Rössler Hyperchaotic System via Sliding Mode Control

2011 ◽  
Vol 66 (1-2) ◽  
pp. 6-12 ◽  
Author(s):  
Jianwen Feng ◽  
Phillip Yam ◽  
Francis Austin ◽  
Chen Xu
Keyword(s):  
Numerical Simulation ◽  
Sliding Mode Control ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Hyperchaotic System ◽  
Mode Control ◽  
Synchronization Problem ◽  
Control Concept ◽  
Simulation Results ◽  
Hyperchaotic Systems

This paper investigates the synchronization problem between two unidirectionally-coupled Rössler hyperchaotic systems in the presence of noise perturbations. Sufficient conditions are obtained for synchronization by using a particularly simple linear sliding mode surface that is based on the sliding mode control concept. Only one controller function is needed to achieve synchronization in our present approach which makes it much easier to implement in contrast to many other synchronization schemes that require two or more controllers. Numerical simulation results are also included to illustrate the superior features of this new scheme.

scholarly journals Discrete Sliding Mode Control for Chaos Synchronization and Its Application to an Improved El-Gamal Cryptosystem

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 843 ◽  
Author(s):  
Pei-Yen Wan ◽  
Teh-Lu Liao ◽  
Jun-Juh Yan ◽  
Hsin-Han Tsai
Keyword(s):  
Chaos Synchronization ◽  
Sliding Mode ◽  
Encryption Algorithm ◽  
Public Key ◽  
Public And Private ◽  
The Public ◽  
Encryption And Decryption ◽  
Asymmetric Encryption ◽  
Improved Design ◽  
Discrete Sliding Mode Control

This paper is concerned with the design of an improved El-Gamal cryptosystem based on chaos synchronization. The El-Gamal cryptosystem is an asymmetric encryption algorithm that must use the public and private keys, respectively, in the encryption and decryption processes. However, in our design, the public key does not have to appear in the public channel. Therefore, this proposed improved El-Gamal cryptosystem becomes a symmetric-like encryption algorithm. First, a discrete sliding mode controller is proposed to ensure the synchronization of master and slave chaotic systems; next, a novel improved El-Gamal cryptosystem is presented. In the traditional El-Gamal cryptosystem, the public key is static and needs to be open which provides an opportunity to attack. However, in this improved design, due to the chaos synchronization, the public key becomes dynamic and does not appear in public channels. As a result, drawbacks of long cipher text and time-consuming calculation in the traditional El-Gamal cryptosystem are all removed. Finally, several performance tests and comparisons have shown the efficiency and security of the proposed algorithm.

scholarly journals Robust Synchronization of Fractional-Order Hyperchaotic Systems Subjected to Input Nonlinearity and Unmatched External Perturbations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Teh-Lu Liao ◽  
Jun-Juh Yan ◽  
Jen-Fuh Chang
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Input Nonlinearity ◽  
Synchronization Problem ◽  
Robust Synchronization ◽  
Single Controller ◽  
Unmatched Uncertainties ◽  
The Cost ◽  
Hyperchaotic Systems ◽  
Control Implementation

This paper investigates the robust synchronization problem for a class of fractional-order hyperchaotic systems subjected to unmatched uncertainties and input nonlinearity. Based on the sliding mode control (SMC) technique, this approach only uses a single controller to achieve chaos synchronization, which reduces the cost and complexity for synchronization control implementation. As expected, the error states can be driven to zero or into predictable bounds for matched and unmatched perturbations, respectively, even with input nonlinearity.

Dynamics of a New 5D Hyperchaotic System of Lorenz Type

2018 ◽  
Vol 28 (03) ◽  
pp. 1850036 ◽  
Author(s):  
Fuchen Zhang ◽  
Rui Chen ◽  
Xingyuan Wang ◽  
Xiusu Chen ◽  
Chunlai Mu ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Chaos Synchronization ◽  
Optimization Theory ◽  
Lyapunov Stability Theory ◽  
Hyperchaotic System ◽  
Ultimate Boundedness ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
Hyperchaotic Systems ◽  
Ultimate Bound

Ultimate boundedness of chaotic dynamical systems is one of the fundamental concepts in dynamical systems, which plays an important role in investigating the stability of the equilibrium, estimating the Lyapunov dimension of attractors and the Hausdorff dimension of attractors, the existence of periodic solutions, chaos control, chaos synchronization. However, it is often difficult to obtain the bounds of the hyperchaotic systems due to the complex algebraic structure of the hyperchaotic systems. This paper has investigated the boundedness of solutions of a nonlinear hyperchaotic system. We have obtained the global exponential attractive set and the ultimate bound set for this system. To obtain the ellipsoidal ultimate bound, the ultimate bound of the proposed system is theoretically estimated using Lagrange multiplier method, Lyapunov stability theory and optimization theory. To show the ultimate bound region, numerical simulations are provided.

SYNCHRONIZATION CONTROL FOR A CLASS OF CHAOTIC SYSTEMS WITH UNCERTAINTIES

2005 ◽  
Vol 15 (07) ◽  
pp. 2235-2246 ◽  
Author(s):  
HER-TERNG YAU ◽  
JUI-SHENG LIN ◽  
JUN-JUH YAN
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Sliding Mode ◽  
Variable Structure ◽  
Synchronization Control ◽  
Control Law ◽  
Structure Control ◽  
Synchronization Problem ◽  
Error State

This paper investigates the chaos synchronization problem for a class of uncertain master-slave chaotic systems. Based on the variable structure control theory, a strategy is proposed to guarantee the occurrence of a sliding mode motion of error states when the proposed control law is applied. As expected, the error state is able to drive to zero with match external uncertainties or into a predictable neighborhood of zero with mismatch external uncertainties. Furthermore, a modified continuous sliding mode controller is also proposed to avoid the chattering. Examples of Lorenz system and Chua's circuit are presented to demonstrate the obtained results.

ANTICIPATED FUNCTION SYNCHRONIZATION WITH UNKNOWN PARAMETERS OF DISCRETE-TIME CHAOTIC SYSTEMS

2009 ◽  
Vol 20 (04) ◽  
pp. 597-608 ◽  
Author(s):  
YIN LI ◽  
BIAO LI ◽  
YONG CHEN
Keyword(s):  
Chaotic System ◽  
Discrete Time ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Law ◽  
Unknown Parameters ◽  
Synchronization Problem ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems ◽  
Function Synchronization

In this paper, firstly, the control problem for the chaos synchronization of discrete-time chaotic (hyperchaotic) systems with unknown parameters are considered. Next, backstepping control law is derived to make the error signals between drive 2D discrete-time chaotic system and response 2D discrete-time chaotic system with two uncertain parameters asymptotically synchronized. Finally, the approach is extended to the synchronization problem for 3D discrete-time chaotic system with two unknown parameters. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.

scholarly journals Passivity-Based Adaptive Hybrid Synchronization of a New Hyperchaotic System with Uncertain Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Xiaobing Zhou ◽  
Zhangbiao Fan ◽  
Dongming Zhou ◽  
Xiaomei Cai
Keyword(s):  
Numerical Simulation ◽  
Parameter Estimation ◽  
Adaptive Control ◽  
Control Theory ◽  
Hyperchaotic System ◽  
Uncertain Parameters ◽  
Synchronization Problem ◽  
Hybrid Synchronization ◽  
New Hyperchaotic System ◽  
Hyperchaotic Systems

We investigate the adaptive hybrid synchronization problem for a new hyperchaotic system with uncertain parameters. Based on the passivity theory and the adaptive control theory, corresponding controllers and parameter estimation update laws are proposed to achieve hybrid synchronization between two identical uncertain hyperchaotic systems with different initial values, respectively. Numerical simulation indicates that the presented methods work effectively.

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