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.

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 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.

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xindong Si ◽  
Hongli Yang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback Control ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Control Law ◽  
Optimization Approach ◽  
Fractional Order Systems ◽  
Linear Feedback Control ◽  
Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

FREQUENCY-DOMAIN CRITERIA FOR GLOBAL SYNCHRONIZATION OF MULTISCROLL CHAOTIC SYSTEMS UNDER LINEAR FEEDBACK CONTROL

2010 ◽  
Vol 20 (07) ◽  
pp. 2165-2177 ◽  
Author(s):  
XIAOFENG WU ◽  
ZHIFANG GUI ◽  
GUANRONG CHEN
Keyword(s):  
Feedback Control ◽  
Frequency Domain ◽  
Chaotic Systems ◽  
Linear Feedback ◽  
Error Feedback ◽  
Linear Feedback Control ◽  
Global Synchronization ◽  
General Mathematical Model ◽  
Linear State ◽  
Absolute Stability Theory

This paper provides a unified approach for achieving and analyzing global synchronization of a class of master-slave coupled multiscroll chaotic systems under linear state-error feedback control. A general mathematical model for such a class of multiscroll chaotic systems is first established. Based on some special properties of such systems, two less-conservative frequency-domain criteria for the desirable global synchronization are rigorously proven by means of the absolute stability theory. The analysis is then applied to two master-slave coupled modified Chua's circuits, obtaining the corresponding simple and precise algebraic criteria for global synchronization, which are finally verified by numerical simulations.

Master-Slave Global Synchronization for Froude Pendulums via Linear State Error Feedback Control

2013 ◽  
Vol 275-277 ◽  
pp. 2565-2569
Author(s):  
Lin Xu ◽  
Zhong Liu ◽  
Yun Chen
Keyword(s):  
Feedback Control ◽  
Chaos Synchronization ◽  
Linear Feedback ◽  
Error Feedback ◽  
Linear Feedback Control ◽  
Global Synchronization ◽  
Numerical Example ◽  
Linear State ◽  
Synchronization Scheme ◽  
State Error

This paper deals with the global chaos synchronization of master-slave Froude pendulums coupled by linear state error feedback control. A master-slave synchronization scheme of the Froude pendulums under linear feedback control is presented. Based on this scheme, some sufficient criteria for global synchronization are proved and optimized. A numerical example is provided to demonstrate the effectiveness of the criteria obtained.

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