A Novel Highly Hyperchaotic System and Its Adaptive Control

2016 ◽  
pp. 513-535 ◽  
Author(s):  
Sundarapandian Vaidyanathan
Keyword(s):  
Adaptive Control ◽  
Hyperchaotic System

scholarly journals Adaptive Control of a Four-Dimensional Hyperchaotic System

2019 ◽  
pp. 1-17
Author(s):  
Xuxia Li ◽  
Xinghua Fan ◽  
Jiuli Yin ◽  
Ying Zhang ◽  
Xiangxiang Lv
Keyword(s):  
Adaptive Control ◽  
Feedback Control ◽  
Control Method ◽  
Adaptive Controller ◽  
Linear Feedback ◽  
Hyperchaotic System ◽  
Linear Feedback Control ◽  
Adaptive Law ◽  
Unstable Equilibrium Point ◽  
Lyapunov Exponent Spectrum

This paper concerns the application of adaptive control method in a four-dimensional hyperchaoticsystem. Firstly, we carry out a systematic dynamic analysis including the properties of equilibriumpoint, stability, dissipation, Lyapunov exponent spectrum, and bifurcation. Both the existenceof two positive Lyapunov exponents and the Lyapunov dimension value show the hyperchaotic property of the system. Based on Lyapunov stability theorem, we then construct an adaptive controller and the adaptive law to suppress hyperchaos to the origin, which is an unstable equilibrium point under a certain parameter set. The effectiveness of the adaptive control is veried by theoretical analysis and numerical simulation. We nally brie y demonstrate the control eciency of self-linear feedback control and misaligned feedback control. For the fourdimensional hyperchaotic system, the adaptive control outperforms them from the view of control speed.

scholarly journals A research on adaptive control to stabilize and synchronize a hyperchaotic system with uncertain parameters

2015 ◽  
Vol 5 (2) ◽  
pp. 51-62 ◽  
Author(s):  
Israr Ahmad ◽  
Azizan Bin Saaban ◽  
Adyda Binti Ibrahim ◽  
Said Al-Hadhrami ◽  
Mohammad Shahzad ◽  
...  
Keyword(s):  
Adaptive Control ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Hyperchaotic System ◽  
Uncertain Parameters ◽  
Closed Loop System ◽  
Complete Synchronization ◽  
Nonlinear Controllers ◽  
Control And Synchronization ◽  
Hyperchaotic Systems

This paper addresses the chaos control and synchronization problems of a hyperchaotic system. It is assumed that the parameters of the hyperchaotic system are unknown and the system is perturbed by the external disturbance. Based on the Lyapunov stability theory and the adaptive control theory, suitable nonlinear controllers are designed for the asymptotic stability of the closed-loop system both for stabilization of hyperchaos at the origin and complete synchronization of two identical hyperchaotic systems. Accordingly, suitable update laws are proposed to estimate the fully uncertain parameters. All simulation results are carried out to validate the effectiveness of the theoretical findings. The effect of external disturbance is under our discussion.

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