scholarly journals An Approach of Tracking Control for Chaotic Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Jin Xing ◽  
Fangfang Zhang
Keyword(s):  
Asymptotic Stability ◽  
Numerical Simulations ◽  
Tracking Control ◽  
Chaotic Systems ◽  
Jacobian Matrix ◽  
Reference Signal ◽  
Projective Synchronization ◽  
Globally Asymptotic Stability ◽  
Control Scheme ◽  
Tracking Controller

Combining the ergodicity of chaos and the Jacobian matrix, we design a general tracking controller for continuous and discrete chaotic systems. The control scheme has the ability to track a bounded reference signal. We prove its globally asymptotic stability and extend it to generalized projective synchronization. Numerical simulations verify the effectiveness of the proposed scheme.

TRACKING CONTROL FOR A CLASS OF CHAOTIC SYSTEMS

2008 ◽  
Vol 22 (12) ◽  
pp. 1977-1984
Author(s):  
XINGYUAN WANG ◽  
MINGJUN WANG
Keyword(s):  
Numerical Simulations ◽  
Control Strategy ◽  
Output Signal ◽  
Tracking Control ◽  
Chaotic Systems ◽  
Control Parameters ◽  
Error Signal ◽  
Reference Signals ◽  
Tracking Controller

This paper presents a tracking control strategy for a class of chaotic systems. A general tracking controller is designed. It is proved theoretically that the error signal can exponentially converge to zero. Numerical simulations show that the controller can make the output signal track all kinds of reference signals. Besides, a better effect can be obtained via changing the control parameters properly.

ACTIVE TRACKING CONTROL OF THE HYPERCHAOTIC LORENZ SYSTEM

2008 ◽  
Vol 22 (19) ◽  
pp. 1859-1865 ◽  
Author(s):  
XINGYUAN WANG ◽  
DAHAI NIU ◽  
MINGJUN WANG
Keyword(s):  
Numerical Simulation ◽  
Tracking Control ◽  
Chaotic Systems ◽  
Lorenz System ◽  
The Self ◽  
Hyperchaotic System ◽  
Reference Signals ◽  
Tracking Controller ◽  
Hyperchaotic Lorenz System ◽  
Simulation Results

A nonlinear active tracking controller for the four-dimensional hyperchaotic Lorenz system is designed in the paper. The controller enables this hyperchaotic system to track all kinds of reference signals, such as the sinusoidal signal. The self-synchronization of the hyperchaotic Lorenz system and the different-structure synchronization with other chaotic systems can also be realized. Numerical simulation results show the effectiveness of the controller.

scholarly journals The Co-existence of Different Synchronization Types in Fractional-order Discrete-time Chaotic Systems with Non–identical Dimensions and Orders

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 710 ◽  
Author(s):  
Samir Bendoukha ◽  
Adel Ouannas ◽  
Xiong Wang ◽  
Amina-Aicha Khennaoui ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Nonlinear Control ◽  
Fractional Order ◽  
Discrete Time ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Generalized Synchronization ◽  
Control Scheme ◽  
Full State ◽  
Hybrid Projective Synchronization ◽  
Inverse Generalized Synchronization

This paper is concerned with the co-existence of different synchronization types for fractional-order discrete-time chaotic systems with different dimensions. In particular, we show that through appropriate nonlinear control, projective synchronization (PS), full state hybrid projective synchronization (FSHPS), and generalized synchronization (GS) can be achieved simultaneously. A second nonlinear control scheme is developed whereby inverse full state hybrid projective synchronization (IFSHPS) and inverse generalized synchronization (IGS) are shown to co-exist. Numerical examples are presented to confirm the findings.

Projective Synchronzing a Novel Fractional Hyperchaotic System Based on a Approach Configuring a Special Matrix

2011 ◽  
Vol 308-310 ◽  
pp. 1688-1694
Author(s):  
Jian Bing Hu ◽  
Jian Xiao ◽  
Ling Dong Zhao ◽  
Qiang Jiang
Keyword(s):  
Numerical Simulations ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
New Approach ◽  
Special Matrix

This work presents a new approach configuring a special matrix to design controller for synchronizing fractional chaotic systems. With this method, fractional chaotic projective synchronization is implemented. Numerical simulations confirm the effectiveness of the approach.

Attitude and height tracking control of unmanned helicopters with disturbances via disturbance observer-based composite dynamic surface control

2021 ◽  
pp. 014233122110232
Author(s):  
Xiangyu Wang ◽  
Ling Han ◽  
Jiyu Liu
Keyword(s):  
Tracking Control ◽  
Disturbance Observer ◽  
Control Design ◽  
Dynamic Surface Control ◽  
Control Technique ◽  
Tracking Errors ◽  
Dynamic Surface ◽  
Surface Control ◽  
Control Scheme ◽  
Tracking Controller

In this paper, the attitude and height tracking control problem is studied for unmanned helicopters with disturbances. To solve the problem, a composite control scheme is proposed based on the combination of dynamic surface control and disturbance observer-based control techniques. The control design includes two parts. In the first part, some nonlinear disturbance observers are designed to accurately estimate the helicopter’s disturbances in different channels. In the second part, based on the disturbance estimates and dynamic surface control technique, a composite dynamic surface tracking controller is designed. Under the proposed composite controller, the attitude and height tracking errors are uniformly ultimately bounded and they can be regulated to be very small by selecting proper controller parameters. For one thing, the proposed control scheme avoids “explosion of terms”, which generally exists in conventional backstepping control and provides a simpler control design. For another thing, without sacrificing the nominal control performances, the anti-disturbance ability of the closed-loop helicopter system is enhanced by using disturbance observers and feedforward compensations. Numerical simulations demonstrate the effectiveness and advantages of the proposed composite tracking controller.

scholarly journals Synchronization methods for chaotic systems involving fractional derivative with a non-singular kernel.

2020 ◽  
Author(s):  
Fatiha Mesdoui ◽  
Nabil Shawagfeh ◽  
Adel Ouannas
Keyword(s):  
Fractional Derivative ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Projective Synchronization ◽  
Singular Kernel ◽  
Lyapunov Theorem ◽  
Control Scheme ◽  
Different Dimensions ◽  
The Lorenz System ◽  
Liu System

This study considers the problem of control-synchronization for chaotic systems involving fractional derivative with a non-singular kernel. Using an extension of the Lyapunov Theorem for systems with Atangana-Baleanu-Caputo (ABC) derivative, a suitable control scheme is designed to achieve matrix projective synchronization (MP) between nonidentical ABC systems with different dimensions. The results are exemplified by the ABC version of the Lorenz system, Bloch system, and Liu system. To show the effectiveness of the proposed results, numerical simulations are performed based on the Adams-Bashforth-Mounlton numerical algorithm.

TRACKING CONTROL AND THE BACKSTEPPING DESIGN OF SYNCHRONIZATION CONTROLLER FOR CHEN SYSTEM

2011 ◽  
Vol 25 (28) ◽  
pp. 3815-3824 ◽  
Author(s):  
XINGYUAN WANG ◽  
JING ZHANG
Keyword(s):  
Numerical Simulations ◽  
Tracking Control ◽  
Design Method ◽  
Backstepping Design ◽  
Error Signal ◽  
Chen System ◽  
Tracking Controller ◽  
Control And Synchronization

This paper presents tracking control and synchronization strategies for Chen system. Two universal controllers, a tracking controller and a synchronization controller based on Backstepping design method were designed. It is proved theoretically that the tracking controller enables the error signal exponentially to converge to zero. The validity of Backstepping synchronization controller is also proved. Numerical simulations further validated the two controllers.

Function Projective Synchronization in Complex Dynamical Networks

2014 ◽  
Vol 926-930 ◽  
pp. 1939-1942 ◽  
Author(s):  
Feng Ling Jia
Keyword(s):  
Numerical Simulations ◽  
Stability Theory ◽  
Complex Dynamical Networks ◽  
Projective Synchronization ◽  
Effective Control ◽  
Dynamical Networks ◽  
Function Projective Synchronization ◽  
Fractional Order Differential Equations ◽  
Control Scheme ◽  
The Stability

In this paper, the function projective synchronization of complex dynamical networks is investigated. Based on the stability theory for fractional-order differential equations, an effective control scheme is proposed to achieve function projective synchronization for complex dynamical networks. Corresponding numerical simulations are presented to show the effectiveness of the proposed synchronization criteria.

scholarly journals An Adaptive Tracking Control of Fractional-Order Chaotic Systems with Uncertain System Parameter

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Ping Zhou ◽  
Rui Ding
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Tracking Control ◽  
System Parameter ◽  
Chaotic Systems ◽  
Reference Signal ◽  
Uncertain System ◽  
Uncertain Parameter ◽  
Adaptive Tracking Control ◽  
Adaptive Tracking

An adaptive tracking control scheme is presented for fractional-order chaotic systems with uncertain parameter. It is theoretically proved that this approach can make the uncertain parameter fractional-order chaotic system track any given reference signal and the uncertain system parameter is estimated through the adaptive tracking control process. Furthermore, the reference signal may belong to other integer-orders chaotic system or belong to different fractional-order chaotic system with different fractional orders. Two examples are presented to demonstrate the effectiveness of the proposed method.

scholarly journals Chaotic Control and Generalized Synchronization for a Hyperchaotic Lorenz-Stenflo System

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Yin Li ◽  
Yulin Zhao ◽  
Zheng-an Yao
Keyword(s):  
Feedback Control ◽  
Numerical Simulations ◽  
Tracking Control ◽  
Unstable Equilibrium ◽  
Generalized Synchronization ◽  
Chaotic Control ◽  
Control Scheme ◽  
Tracking Controllers ◽  
Tracking Model

This paper is devoted to investigate the tracking control and generalized synchronization of the hyperchaotic Lorenz-Stenflo system using the tracking model and the feedback control scheme. We suppress the chaos to unstable equilibrium via three feedback methods, and we achieve three globally generalized synchronization controls. Novel tracking controllers with corresponding parameter update laws are designed such that the Lorenz-Stenflo systems can be synchronized asymptotically. Moreover, numerical simulations are presented to demonstrate the effectiveness, through the contrast between the orbits before being stabilized and the ones after being stabilized.

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