scholarly journals Adaptive Terminal Synergetic Synchronization of Hyperchaotic Systems

2021 ◽  
Vol 54 (5) ◽  
pp. 789-795
Author(s):  
Yamina Haddadji ◽  
Mohamed Naguib Harmas ◽  
Abdlouahab Bouafia ◽  
Ziyad Bouchama
Keyword(s):  
Nonlinear Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
Slave System ◽  
Unknown Parameters ◽  
Master System ◽  
Simulation Results ◽  
Hyperchaotic Systems

This research paper introduces an adaptive terminal synergetic nonlinear control. This control aims at synchronizing two hyperchaotic Zhou systems. Thus, the adaptive terminal synergetic control’s synthesis is applied to synchronize a hyperchaotic i.e., slave system with unknown parameters with another hyperchaotic i.e., master system. Accordingly, simulation results of each system in different initial conditions reveal significant convergence. Moreover, the findings proved stability and robustness of the suggested scheme using Lyapunov stability theory.

Adaptive Attitude Control on Multiple Independently Targeted Reentry Vehicles (MIRV)

2014 ◽  
Vol 494-495 ◽  
pp. 1316-1319
Author(s):  
Xing Yu Chen ◽  
Fan Li ◽  
Jian Hui Zhao ◽  
Zhao Long Fan
Keyword(s):  
Numerical Simulation ◽  
Control System ◽  
Lyapunov Stability ◽  
Attitude Control ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Attitude Dynamics ◽  
Dynamics Model ◽  
Simulation Results

Based on the characteristics of releasing loads for many times, the attitude dynamics model of MIRV has established by using the Rodrigues representation, and we proposed a method of indirect multi-model adaptive attitude control. It was proved that the adaptive controller we designed can ensure the control system globally uniformly and bounded stable according to the Lyapunov stability theory, and the effectiveness of the controller was demonstrated by the numerical simulation results.

ADAPTIVE SYNCHRONIZATION OF A NOVEL HYPERCHAOTIC SYSTEM WITH FULLY UNKNOWN PARAMETERS

2013 ◽  
Vol 27 (32) ◽  
pp. 1350197
Author(s):  
XING-YUAN WANG ◽  
SI-HUI JIANG ◽  
CHAO LUO
Keyword(s):  
Lyapunov Stability ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Chaotic Synchronization ◽  
Adaptive Synchronization ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
Chen System ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems

In this paper, a chaotic synchronization scheme is proposed to achieve adaptive synchronization between a novel hyperchaotic system and the hyperchaotic Chen system with fully unknown parameters. Based on the Lyapunov stability theory, an adaptive controller and parameter updating law are presented to synchronize the above two hyperchaotic systems. The corresponding theoretical proof is given and numerical simulations are presented to verify the effectiveness of the proposed scheme.

SYNCHRONIZATION OF UNCERTAIN HYPERCHAOTIC AND CHAOTIC SYSTEMS BY ADAPTIVE CONTROL

2008 ◽  
Vol 18 (12) ◽  
pp. 3731-3736 ◽  
Author(s):  
ZHI-YU LIU ◽  
CHIA-JU LIU ◽  
MING-CHUNG HO ◽  
YAO-CHEN HUNG ◽  
TZU-FANG HSU ◽  
...  
Keyword(s):  
Chaotic Systems ◽  
Mean Squared Error ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Slave System ◽  
Unknown Parameters ◽  
Squared Error ◽  
Master System ◽  
Two Systems ◽  
The Mean

This paper presents the synchronization between uncertain hyperchaotic and chaotic systems. Based on Lyapunov stability theory, an adaptive controller is derived to achieve synchronization of hyperchaotic and chaotic systems, including the case of unknown parameters in these two systems. The T.N.Č. hyperchaotic oscillator is used as the master system, and the Rössler system is used as the slave system. Numerical simulations verify these results. Additionally, the effect of noise is investigated by measuring the mean squared error (MSE) of two systems.

Active Anti-Synchronization Between Identical and Distinctive Hyperchaotic Systems

2008 ◽  
Vol 15 (04) ◽  
pp. 371-382 ◽  
Author(s):  
M. M. Al-sawalha ◽  
M. S. M. Noorani
Keyword(s):  
Theoretical Analysis ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
High Dimensional ◽  
Analysis Strategy ◽  
Relevant Variables ◽  
Hyperchaotic Systems

This paper brings attention to hyperchaos anti-synchronization between two identical and distinctive hyperchaotic systems using active control theory. The sufficient conditions for achieving anti-synchronization of two high dimensional hyperchaotic systems is derived based on Lyapunov stability theory, where the controllers are designed by using the sum of relevant variables in hyperchaotic systems. Numerical results are presented to justify the theoretical analysis strategy.

scholarly journals Robust Synchronization of Hyperchaotic Systems with Uncertainties and External Disturbances

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Qing Wang ◽  
Yongguang Yu ◽  
Hu Wang
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Convergence Speed ◽  
External Disturbances ◽  
Adaptive Controllers ◽  
Robust Synchronization ◽  
Hyperchaotic Systems

The robust synchronization of hyperchaotic systems with uncertainties and external disturbances is investigated. Based on the Lyapunov stability theory, the appropriate adaptive controllers and parameter update laws are designed to achieve the synchronization of uncertain hyperchaotic systems. The robust synchronization of two hyperchaotic Chen systems is taken as an example to verify the feasibility of the presented schemes. The size of the subcontroller gain’s influences on the convergence speed is discussed. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed synchronization schemes.

scholarly journals Outer Synchronization of a Modified Quorum-Sensing Network via Adaptive Control

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Jianbao Zhang ◽  
Wenyin Zhang ◽  
Denghua Zhang ◽  
Chengdong Yang ◽  
Kongwei Zhu ◽  
...  
Keyword(s):  
Adaptive Control ◽  
Quorum Sensing ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Negative Effects ◽  
Unknown Parameters ◽  
Adaptive Controllers ◽  
Outer Synchronization ◽  
Noise Disturbances

Motivated by the quorum-sensing mechanism of bacteria, this paper modifies the network model by adding unknown parameters and noise disturbances and investigates the problem of outer synchronization via adaptive control. In case there exist three unknown parameters, updating laws are presented to identify the unknown parameters with help of Lyapunov stability theory, and the negative effects of noise disturbances are also compensated by designing adaptive controllers. In addition, we simplify the obtained conditions and carry out two succinct and utilitarian corollaries. Finally, numerical simulations are provided to show the validity of the obtained results.

scholarly journals Parameter Estimation and Hybrid Lag Synchronization in Hyperchaotic Lü Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qing Wei ◽  
Zuolei Wang
Keyword(s):  
Numerical Simulation ◽  
Parameter Estimation ◽  
Adaptive Control ◽  
Lyapunov Stability ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Unknown Parameters ◽  
Lag Synchronization ◽  
Control Approach ◽  
Simulation Results

The antiphase and complete lag synchronization of hyperchaotic Lü systems with unknown parameters is investigated. Based on the Lyapunov stability theory, the sufficient conditions for achieving hybrid lag synchronization are derived. The optimized parameter observers are approached analytically via adaptive control approach. Numerical simulation results are presented to verify the effectiveness of the proposed scheme.

scholarly journals Synchronization of Fractional-Order Hyperchaotic Systems via Fractional-Order Controllers

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Tianzeng Li ◽  
Yu Wang ◽  
Yong Yang
Keyword(s):  
Fractional Order ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Hyperchaotic System ◽  
Control Parameters ◽  
Optimal Value ◽  
Fractional Order Controller ◽  
Hyperchaotic Systems

In this paper, the synchronization of fractional-order chaotic systems is studied and a new fractional-order controller for hyperchaos synchronization is presented based on the Lyapunov stability theory. The proposed synchronized method can be applied to an arbitrary four-dimensional fractional hyperchaotic system. And we give the optimal value of control parameters to achieve synchronization of fractional hyperchaotic system. This approach is universal, simple, and theoretically rigorous. Numerical simulations of several fractional-order hyperchaotic systems demonstrate the universality and the effectiveness of the proposed method.

ANTI-SYNCHRONIZATION OF UNIFIED HYPERCHAOTIC SYSTEMS

2014 ◽  
Vol 28 (05) ◽  
pp. 1450014
Author(s):  
PI LI ◽  
XING-YUAN WANG ◽  
PENG SUN ◽  
CHAO LUO ◽  
XIU-KUN WANG
Keyword(s):  
Adaptive Control ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Control Methods ◽  
System Parameters ◽  
Hyperchaotic Systems ◽  
Active Control Method

In this paper, active control and adaptive control methods are applied, respectively. Adaptive control method is implemented when system parameters are unknown and active control method is applied when system parameters are known. Based on the Lyapunov stability theory, the controllers are designed to realize anti-synchronization, meanwhile, the update laws of parameters are proposed. The theoretical proof is given. And two groups of examples are shown to verify the effectiveness of the proposed schemes.

scholarly journals Lag Synchronization of Hyperchaotic Systems via Intermittent Control

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Junjian Huang ◽  
Chuandong Li ◽  
Wei Zhang ◽  
Pengcheng Wei ◽  
Qi Han
Keyword(s):  
Theoretical Analysis ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Intermittent Control ◽  
Lag Synchronization ◽  
Control Scheme ◽  
Hyperchaotic Systems ◽  
Theoretical Results

Different from the most existing results, in this paper an intermittent control scheme is designed to achieve lag synchronization of coupled hyperchaotic systems. Several sufficient conditions ensuring lag synchronization are proposed by rigorous theoretical analysis with the help of the Lyapunov stability theory. Numerical simulations are also presented to show the effectiveness and feasibility of the theoretical results.

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