scholarly journals Linear Feedback Synchronization Used in the Three-Dimensional Duffing System

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Jian-qun Han ◽  
Xu-dong Shi ◽  
Hong Sun
Keyword(s):  
Feedback Control ◽  
Chaotic System ◽  
Control Method ◽  
Three Dimensional ◽  
Lyapunov Stability Theory ◽  
Linear Feedback ◽  
Nonlinear Feedback ◽  
Linear Feedback Control ◽  
Duffing System ◽  
Feedback Control Method

It has been realized that synchronization using linear feedback control method is efficient compared to nonlinear feedback control method due to the less computational complexity and the synchronization error. For the problem of feedback synchronization of Duffing chaotic system, in the paper, we firstly established three-dimensional Duffing system by method of variable decomposition and, then, studied the synchronization of Duffing chaotic system and designed the control law based on linear feedback control and Lyapunov stability theory. It is proved theoretically that the two identical integer order chaotic systems are synchronized analytically and numerically.

scholarly journals Stabilization of a Class of Complex Chaotic Systems by the Dynamic Feedback Control

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Zhi Liu ◽  
Rongwei Guo
Keyword(s):  
Feedback Control ◽  
Chaotic System ◽  
Control Method ◽  
Linear Feedback ◽  
Dynamic Feedback ◽  
Feedback Control Method ◽  
Dynamic Feedback Control ◽  
Complex Chaotic Systems ◽  
Complex Chaotic System ◽  
Theoretical Results

The stabilization problem of the complex chaotic system is investigated in this paper. First, a systematic method is proposed, by which a given complex chaotic system can be transformed into its equivalent real chaotic system. Then, both simple and physical controller is designed for the corresponding real chaotic system by the dynamic feedback control method, thereby the controller for the original complex chaotic system is obtained. Especially, for some complex system, the controller is obtained by the linear feedback control method. Finally, two illustrative examples with numerical simulations are used to verify the validity and effectiveness of the theoretical results.

scholarly journals Mixed Synchronization of Chaotic Financial Systems by Using Linear Feedback Control

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Ke Ding ◽  
Xing Xu
Keyword(s):  
Feedback Control ◽  
Control Method ◽  
Linear Feedback ◽  
Financial Systems ◽  
Linear Feedback Control ◽  
Single Controller

This paper deals with the mixed synchronization (coexistence of synchronization and antisynchronization) of two chaotic financial systems. Two mixed synchronization criteria for two chaotic financial systems are derived with a single controller and without external controls, respectively. In addition, the control method and synchronization criteria are applied to study the mixed synchronization of a class of modified chaotic financial systems. Three examples are used to illustrate the effectiveness of our derived results.

CONTROLLING UNCERTAIN VAN DER POL OSCILLATOR VIA ROBUST NONLINEAR FEEDBACK CONTROL

2004 ◽  
Vol 14 (05) ◽  
pp. 1671-1681 ◽  
Author(s):  
MAO-YIN CHEN ◽  
ZHENG-ZHI HAN ◽  
YUN SHANG ◽  
GUANG-DENG ZONG
Keyword(s):  
Feedback Control ◽  
Control Method ◽  
Reference Signal ◽  
Variable Structure ◽  
Van Der Pol Oscillator ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Van Der Pol ◽  
Feedback Control Method ◽  
System Uncertainties

Combining the backstepping design and the variable structure control, we propose a robust nonlinear feedback control method to control an uncertain van der Pol oscillator even if there exist system uncertainties and external disturbances in this oscillator. If system uncertainties are estimated and some parameters are chosen suitably, the output of van der Pol osicllator can track arbitrary smooth reference signal. Theoretical analysis and numerical simulations verify the effectiveness of this method.

scholarly journals Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Jing Wang ◽  
Shaojuan Ma ◽  
Peng Hao ◽  
Hehui Yuan
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Control Method ◽  
Magnetic Bearing ◽  
Uncertain Parameter ◽  
Equivalent Model ◽  
Linear Feedback ◽  
Feedback Control Method ◽  
And Control ◽  
Bearing System

In this paper, the Hopf bifurcation and control of the magnetic bearing system under an uncertain parameter are investigated. Firstly, the two-degree-of-freedom magnetic bearing system model with uncertain parameter is established. The method of orthogonal polynomial approximation is used to obtain the equivalent magnetic bearing model which is deterministic. Secondly, combining mathematical analysis tools and numerical simulations, the Hopf bifurcation of the equivalent model is analyzed. Finally, a hybrid feedback control method (linear feedback control method combined with nonlinear stochastic feedback control method) is introduced to control the Hopf bifurcation behavior of the magnetic bearing system.

Sign in / Sign up

Export Citation Format

Share Document