CHAOS MULTISCALE-SYNCHRONIZATION BETWEEN TWO DIFFERENT FRACTIONAL-ORDER HYPERCHAOTIC SYSTEMS BASED ON FEEDBACK CONTROL

2013 ◽  
Vol 23 (08) ◽  
pp. 1350146 ◽  
Author(s):  
LIN PAN ◽  
ZHIHONG GUAN ◽  
LONG ZHOU
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Control Method ◽  
Hyperchaotic System ◽  
Nonlinear Feedback ◽  
Control Functions ◽  
Short Period ◽  
Feedback Control Method ◽  
Linear And Nonlinear ◽  
Hyperchaotic Systems

In this paper, the chaos multiscale-synchronization between two different Fractional-order Hyperchaotic System (FOHCS)s have been investigated. The Lü-like and its FOHCS are also studied. The Lü-like FOHCS is controlled to be multiscale-synchronization with Liu FOHCS and new Lorenz FOHCS, respectively. The analytical conditions for the multiscale-synchronization of these pairs of different FOHCSs are derived by utilizing Laplace transform. Furthermore, multiscale-synchronization between two different FOHCSs is achieved by utilizing the different linear and nonlinear feedback control method in a short period and both remain in chaotic states. Numerical simulations are used to verify the theoretical analysis using different values of the fractional-order parameter and the different linear and nonlinear control functions.

scholarly journals Antisynchronization of the Hyperchaotic Systems with Uncertainty and Disturbance Using the UDE-Based Control Method

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Zuoxun Wang ◽  
Xiaotong Yu ◽  
Guijuan Wang
Keyword(s):  
Feedback Control ◽  
Control Method ◽  
External Disturbance ◽  
Hyperchaotic System ◽  
Dynamic Feedback ◽  
Disturbance Estimation ◽  
Feedback Control Method ◽  
Dynamic Feedback Control ◽  
Hyperchaotic Systems ◽  
Uncertainty And Disturbance Estimation

In this paper, we investigate the antisynchronization problem of a class of hyperchaotic systems with both model uncertainty and external disturbance. Firstly, combining the dynamic feedback control method and the uncertainty and disturbance estimation (UDE)-based control method, we propose a new UDE-based dynamic feedback control method. Secondly, we take the 4D hyperchaotic system as an example and realize the antisynchronization problem of such system. Finally, the effectiveness and correctness of the proposed method is verified by numerical simulation.

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 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 Partial Anti-Synchronization of the Fractional-Order Chaotic Systems through Dynamic Feedback Control

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 718
Author(s):  
Runlong Peng ◽  
Cuimei Jiang ◽  
Rongwei Guo
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Dynamic Feedback ◽  
Synchronization Problem ◽  
Feedback Control Method ◽  
Single Input ◽  
Dynamic Feedback Control ◽  
Necessary And Sufficient

This paper investigates the partial anti-synchronization problem of fractional-order chaotic systems through the dynamic feedback control method. Firstly, a necessary and sufficient condition is proposed, by which the existence of the partial anti-synchronization problem is proved. Then, an algorithm is given and used to obtain all solutions of this problem. Moreover, the partial anti-synchronization problem of the fractional-order chaotic systems is realized through the dynamic feedback control method. It is noted that the designed controllers are single-input controllers. Finally, two illustrative examples with numerical simulations are used to verify the correctness and effectiveness of the proposed results.

scholarly journals Synchronization of Fractional-Order Chaotic Systems with Model Uncertainty and External Disturbance

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 877
Author(s):  
Rongwei Guo ◽  
Yaru Zhang ◽  
Cuimei Jiang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Model Uncertainty ◽  
Chaotic Systems ◽  
Control Method ◽  
External Disturbance ◽  
Dynamic Feedback ◽  
Complete Synchronization ◽  
Feedback Control Method ◽  
Dynamic Feedback Control

This paper is concerned with complete synchronization of fractional-order chaotic systems with both model uncertainty and external disturbance. Firstly, we propose a new dynamic feedback control method for complete synchronization of fractional-order nominal systems (without both uncertainty and disturbance). Then, a new uncertainty and disturbance estimator (UDE)-based dynamic feedback control method for the fractional-order systems with both uncertainty and disturbance is presented, by which the synchronization problem of such fractional-order chaotic systems is realized. Finally, the fractional-order Lorenz system is used to demonstrate the practicability of the proposed results.

scholarly journals State-Feedback Control for Fractional-Order Nonlinear Systems Subject to Input Saturation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Junhai Luo
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
State Feedback ◽  
Control Method ◽  
Input Saturation ◽  
State Feedback Control ◽  
Sufficient Condition ◽  
Feedback Control Method ◽  
Linear State

We give a state-feedback control method for fractional-order nonlinear systems subject to input saturation. First, a sufficient condition is derived for the asymptotical stability of a class of fractional-order nonlinear systems. Then based on Gronwall-Bellman lemma and a sector bounded condition of the saturation function, a linear state-feed back controller is designed. Finally, two simulation examples are presented to show the validity of the proposed method.

Chaos, Sliding Mode Control between Two Different Fractional-Order Hyperchaotic Systems with Uncertain Parameters

2012 ◽  
Vol 424-425 ◽  
pp. 318-323
Author(s):  
Hong Zhang ◽  
Dao Yin Qiu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Control Method ◽  
Sliding Mode ◽  
Order System ◽  
Hyperchaotic System ◽  
Uncertain Parameters ◽  
Mode Control ◽  
Short Period ◽  
The Stability

This work investigates chaos synchronization between two different fractional-order hyperchaotic system (FOHS)s with uncertain parameters. The Chen FOHS is controlled to be synchronized with a new FOHS. The analytical conditions for the synchronization of different FOHSs are derived by utilizing the stability theory of fractional-order system. Furthermore, synchronization between two different FOHSs is achieved by utilizing sliding mode control method in a quite short period and both remain in chaotic states. Numerical simulations are used to verify the theoretical analysis using different values of the fractional-order parameter

scholarly journals Two Types of Synchronization Problems in a New 5D Hyperchaotic System

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Bin Li ◽  
Xue Yang ◽  
Qixing Liang ◽  
Zhi Li
Keyword(s):  
Feedback Control ◽  
Control Method ◽  
Hyperchaotic System ◽  
Dynamic Feedback ◽  
Complete Synchronization ◽  
Synchronization Problem ◽  
Feedback Control Method ◽  
Dynamic Feedback Control ◽  
Theoretical Results ◽  
Synchronization Problems

This paper investigates the synchronization problem in a new 5D hyperchaotic system. Firstly, the existence of two types of synchronization problems in the new 5D hyperchaotic system is proved. Then, by the dynamic feedback control method, one complete synchronization problem and three coexistence of complete synchronization and antisynchronization problems in such system are realized. Finally, numerical simulations are used to verify the validity and effectiveness of the theoretical results.

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