scholarly journals Projective Synchronization ofN-Dimensional Chaotic Fractional-Order Systems via Linear State Error Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Baogui Xin ◽  
Tong Chen
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Projective Synchronization ◽  
Control Technique ◽  
Linear Feedback ◽  
Fractional Order Systems ◽  
Financial Systems ◽  
Linear State ◽  
Synchronization Scheme ◽  
State Error

Based on linear feedback control technique, a projective synchronization scheme ofN-dimensional chaotic fractional-order systems is proposed, which consists of master and slave fractional-order financial systems coupled by linear state error variables. It is shown that the slave system can be projectively synchronized with the master system constructed by state transformation. Based on the stability theory of linear fractional order systems, a suitable controller for achieving synchronization is designed. The given scheme is applied to achieve projective synchronization of chaotic fractional-order financial systems. Numerical simulations are given to verify the effectiveness of the proposed projective synchronization scheme.

scholarly journals Synchronization of Chaotic Fractional-Order WINDMI Systems via Linear State Error Feedback Control

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Baogui Xin ◽  
Tong Chen ◽  
Yanqin Liu
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Chaos Synchronization ◽  
Control Technique ◽  
Order System ◽  
Error Feedback ◽  
Linear State ◽  
The Stability ◽  
Synchronization Scheme ◽  
State Error

We propose a fractional-order WINDMI system, as a generalization of an integer-order system developed by Sprott (2003). The considered synchronization scheme consists of identical master and slave fractional-order WINDMI systems coupled by linear state error variables. Based on the stability theory of nonlinear fractional-order systems, linear state error feedback control technique is applied to achieve chaos synchronization, and a linear control law is derived analytically to achieve synchronization of the chaotic fractional-order WINDMI system. Numerical simulations validate the main results of this work.

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.

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.

PROJECTIVE SYNCHRONIZATION OF FRACTIONAL ORDER CHAOTIC SYSTEMS BASED ON STATE OBSERVER

2012 ◽  
Vol 26 (30) ◽  
pp. 1250176 ◽  
Author(s):  
XING-YUAN WANG ◽  
ZUN-WEN HU
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
State Observer ◽  
Projective Synchronization ◽  
Pole Placement ◽  
Fractional Order Systems ◽  
Chen System ◽  
The Stability ◽  
Synchronization Scheme ◽  
Placement Technique

Based on the stability theory of fractional order systems and the pole placement technique, this paper designs a synchronization scheme with the state observer method and achieves the projective synchronization of a class of fractional order chaotic systems. Taking an example for the fractional order unified system by using this observer controller, and numerical simulations of fractional order Lorenz-like system, fractional order Lü system and fractional order Chen system are provided to demonstrate the effectiveness of the proposed scheme.

Hybrid Projective Synchronization of Complex Dynamical Networks with Fractional-Order System Nodes

2013 ◽  
Vol 336-338 ◽  
pp. 2365-2368
Author(s):  
Fan Di Zhang
Keyword(s):  
Fractional Order ◽  
Complex Dynamical Networks ◽  
Projective Synchronization ◽  
Control Technique ◽  
Order System ◽  
Dynamical Networks ◽  
Hybrid Projective Synchronization ◽  
The Stability ◽  
System Nodes ◽  
Synchronization Scheme

This paper investigates the problem of hybrid projective synchronization (HPS) in dynamical networks with fractional-order hyper-chaotic system nodes. Based on the stability analysis of fractional-order systems and nonlinear control technique, we propose a novel and general approach to realize the synchronization of complex network. A nonlinear controllers are designed to make the fractional-order complex dynamical networks with distinct nodes asymptotically synchronize onto any smooth goal dynamics. Numerical simulations are presented to demonstrate the effectiveness of the proposed synchronization scheme.

scholarly journals Hybrid Projective Synchronization of Fractional-Order Chaotic Systems with Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Li-xin Yang ◽  
Jun Jiang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Pole Placement ◽  
Fractional Order Systems ◽  
Hybrid Projective Synchronization ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems ◽  
Placement Technique

The hybrid projective synchronization for fractional-order chaotic systems with time delay is investigated in this paper. On the basis of stability analysis of fractional-order systems and pole placement technique, a novel and general approach is proposed. The hybrid projective synchronization of fractional-order chaotic and hyperchaotic systems with time delay is achieved via designing an appropriate controller. Corresponding numerical results are presented to demonstrate the effectiveness of the proposed synchronization scheme. Furthermore, the influence of the fractional order on the synchronization process is discussed. The result reveals that the fractional order has a significant effect on the synchronization speed.

scholarly journals Modified Function Projective Synchronization between Different Dimension Fractional-Order Chaotic Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Ping Zhou ◽  
Rui Ding
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Fractional Order Systems ◽  
Fractional Order Derivative ◽  
Function Projective Synchronization ◽  
Modified Function Projective Synchronization ◽  
Synchronization Scheme

A modified function projective synchronization (MFPS) scheme for different dimension fractional-order chaotic systems is presented via fractional order derivative. The synchronization scheme, based on stability theory of nonlinear fractional-order systems, is theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed method.

scholarly journals Hybrid Projective Synchronization for Two Identical Fractional-Order Chaotic Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Ping Zhou ◽  
Rui Ding ◽  
Yu-xia Cao
Keyword(s):  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Fractional Order Systems ◽  
Response System ◽  
Hyperchaotic Lu System ◽  
Hybrid Projective Synchronization ◽  
The Stability ◽  
Synchronization Scheme

A hybrid projective synchronization scheme for two identical fractional-order chaotic systems is proposed in this paper. Based on the stability theory of fractional-order systems, a controller for the synchronization of two identical fractional-order chaotic systems is designed. This synchronization scheme needs not to absorb all the nonlinear terms of response system. Hybrid projective synchronization for the fractional-order Chen chaotic system and hybrid projective synchronization for the fractional-order hyperchaotic Lu system are used to demonstrate the validity and feasibility of the proposed scheme.

On an Optimal Control Applied in Atomic Force Microscopy (AFM) Including Fractional-Order

2017 ◽  
Author(s):  
Angelo M. Tusset ◽  
Jose M. Balthazar ◽  
Jeferson Jose de Lima ◽  
Rodrigo T. Rocha ◽  
Frederic C. Janzen ◽  
...  
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Nonlinear Behavior ◽  
Control Technique ◽  
Linear Feedback ◽  
Squeeze Film ◽  
Good Tool ◽  
Chaotic Motions ◽  
Atomic Force ◽  
Squeeze Film Damping

In this work, the nonlinear dynamics of an Atomic Force Microscope (AFM) operating in tapping mode is investigated, considering the influence of squeeze film damping in fractional-order. Its influence plays an important role because the dynamics of the AFM can be led to different responses, e.g., periodic and chaotic motions, specially the influence of the derivative order when in fractional-order. In a way to characterize the type of behavior, the 0–1 test was used once this is a good tool to characterize fractional-order differential systems. In addition, the linear feedback control technique for fractional-order systems is applied to control the chaotic behaviors. Therefore, the results showed a nonlinear behavior presented by the AFM system. In addition, the feedback control technique was efficient to control the chaotic motion of the micro cantilever beam of the AFM, whose results included variation of parameters of the fractional derivative of the squeeze film damping.

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