Control Fractional-Order Continuous Chaotic System via a Simple Fractional-Order Controller

2013 ◽  
Vol 336-338 ◽  
pp. 770-773
Author(s):  
Dong Zhang ◽  
Shou Liang Yang
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Stability Theorem ◽  
Asymptotically Stable ◽  
Fractional Order Systems ◽  
Control Scheme ◽  
The Stability ◽  
Fractional Order Controller ◽  
Order Continuous

A universal fractional-order controller is proposed to asymptotically stable the unstable equilibrium points and the nonequilibrium points of continuous fractional-order chaos systems. The simple fractional-order controller is obtained based on the stability theorem of nonlinear fractional-order systems. The control scheme is simple and theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed fractional-order controller.

Anti-Synchronization Control of the Complex Lu System

2014 ◽  
Vol 721 ◽  
pp. 269-272
Author(s):  
Fan Di Zhang
Keyword(s):  
Complex System ◽  
Fractional Order ◽  
Control Strategy ◽  
Stability Theorem ◽  
Projective Synchronization ◽  
Synchronization Control ◽  
Fractional Order Systems ◽  
Lü System ◽  
The Stability ◽  
Lu System

This paper propose fractional-order Lu complex system. Moreover, projective synchronization control of the fractional-order hyper-chaotic complex Lu system is studied based on feedback technique and the stability theorem of fractional-order systems, the scheme of anti-synchronization for the fractional-order hyper-chaotic complex Lu system is presented. Numerical simulations on examples are presented to show the effectiveness of the proposed control strategy.

Investigation of Synchronization for a Fractional-Order Delayed System

2014 ◽  
Vol 687-691 ◽  
pp. 447-450 ◽  
Author(s):  
Hong Gang Dang ◽  
Wan Sheng He ◽  
Xiao Ya Yang
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Fractional Order Systems ◽  
Delayed System ◽  
The Stability

In this paper, synchronization of a fractional-order delayed system is studied. Based on the stability theory of fractional-order systems, by designing appropriate controllers, the synchronization for the proposed system is achieved. Numerical simulations show the effectiveness of the proposed scheme.

scholarly journals Adaptive - Synchronization of Fractional-Order Chaotic Systems with Nonidentical Structures

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Li-xin Yang ◽  
Wan-sheng He
Keyword(s):  
Adaptive Control ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Technique ◽  
Adaptive Synchronization ◽  
Fractional Order Systems ◽  
The Stability ◽  
Different Chaotic Systems ◽  
Theoretical Results

This paper investigates the adaptive - synchronization of the fractional-order chaotic systems with nonidentical structures. Based on the stability of fractional-order systems and adaptive control technique, a general formula for designing the controller and parameters update law is proposed to achieve adaptive - synchronization between two different chaotic systems with different structures. The effective scheme parameters identification and - synchronization of chaotic systems can be realized simultaneously. Furthermore, two typical illustrative numerical simulations are given to demonstrate the effectiveness of the proposed scheme, for each case, we design the controller and parameter update laws in detail. The numerical simulations are performed to verify the effectiveness of the theoretical results.

LAG SYNCHRONIZATION OF THE FRACTIONAL-ORDER SYSTEM VIA NONLINEAR OBSERVER

2011 ◽  
Vol 25 (29) ◽  
pp. 3951-3964 ◽  
Author(s):  
HAO ZHU ◽  
ZHONGSHI HE ◽  
SHANGBO ZHOU
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Stability Theorem ◽  
Nonlinear Observer ◽  
Order System ◽  
Fractional Order Systems ◽  
Lag Synchronization ◽  
Systematic Method ◽  
Fractional System ◽  
The Stability

In this paper, based on the idea of nonlinear observer, lag synchronization of chaotic fractional system with commensurate and incommensurate order is studied by the stability theorem of linear fractional-order systems. The theoretical analysis of fractional-order systems in this paper is a systematic method. This technique is applied to achieve the lag synchronization of fractional-order Rössler's system, verified by numerical simulation.

Synchronization of a New Fractional Order Hyperchaotic System with Activation Feedback Control

2013 ◽  
Vol 397-400 ◽  
pp. 1278-1281
Author(s):  
Wei Wei Zhang ◽  
Ding Yuan Chen
Keyword(s):  
Feedback Control ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Current Paper ◽  
Hyperchaotic System ◽  
Fractional Order Systems ◽  
The Stability

In the current paper, a new fractional order hyperchaotic system is discussed. Using the activation feedback control, the synchronization of a new fractional order hyperchaotic system is implemented based on the stability theory of fractional order systems. Numerical simulations are demonstrated the effectiveness.

scholarly journals Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Seng-Kin Lao ◽  
Lap-Mou Tam ◽  
Hsien-Keng Chen ◽  
Long-Jye Sheu
Keyword(s):  
Fractional Order ◽  
Design Stage ◽  
Fractional Order Systems ◽  
State Variables ◽  
Driving System ◽  
Control Scheme ◽  
The Stability ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems ◽  
Stability Checking

A hybrid stability checking method is proposed to verify the establishment of synchronization between two hyperchaotic systems. During the design stage of a synchronization scheme for chaotic fractional-order systems, a problem is sometimes encountered. In order to ensure the stability of the error signal between two fractional-order systems, the arguments of all eigenvalues of the Jacobian matrix of the erroneous system should be within a region defined in Matignon’s theorem. Sometimes, the arguments depend on the state variables of the driving system, which makes it difficult to prove the stability. We propose a new and efficient hybrid method to verify the stability in this situation. The passivity-based control scheme for synchronization of two hyperchaotic fractional-order Chen-Lee systems is provided as an example. Theoretical analysis of the proposed method is validated by numerical simulation in time domain and examined in frequency domain via electronic circuits.

Dynamics and Synchronization of the Fractional-Order Sprott E System

2013 ◽  
Vol 850-851 ◽  
pp. 876-879
Author(s):  
Hong Gang Dang
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Attractor ◽  
Fractional Order Systems ◽  
The Stability

In this paper, dynamics and synchronization of the fractional-order Sprott E system are investigated. Firstly, the chaotic attractor of the system is got by means of numerical simulation. Then based on the stability theory of fractional-order systems, the synchronization of the system is realized. Numerical simulations are carried out to demonstrate the effectiveness of the controllers.

scholarly journals Analisis Dinamik Model Transmisi COVID-19 dengan Melibatkan Intervensi Karantina

2021 ◽  
Author(s):  
Resmawan Resmawan ◽  
Agusyarif Rezka Nuha ◽  
Lailany Yahya
Keyword(s):  
Population Dynamics ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Human Class ◽  
Existence Of Equilibrium ◽  
The Stability ◽  
Disease Free

This paper discusses the dynamics of COVID-19 transmission by involving quarantine interventions. The model was constructed by involving three classes of infectious causes, namely the exposed human class, asymptotically infected human class, and symptomatic infected human class. Variables were representing quarantine interventions to suppress infection growth were also considered in the model. Furthermore, model analysis is focused on the existence of equilibrium points and numerical simulations to visually showed population dynamics. The constructed model forms the SEAQIR model which has two equilibrium points, namely a disease-free equilibrium point and an endemic equilibrium point. The stability analysis showed that the disease-free equilibrium point was locally asymptotically stable at R0<1 and unstable at R0>1. Numerical simulations showed that increasing interventions in the form of quarantine could contribute to slowing the transmission of COVID-19 so that it is hoped that it can prevent outbreaks in the population.

scholarly journals Analisis Dinamik Model Transmisi COVID-19 dengan Melibatkan Intervensi Karantina

2021 ◽  
Vol 3 (1) ◽  
pp. 66-79
Author(s):  
Resmawan Resmawan ◽  
Agusyarif Rezka Nuha ◽  
Lailany Yahya
Keyword(s):  
Population Dynamics ◽  
Numerical Simulations ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Human Class ◽  
Existence Of Equilibrium ◽  
Visual Model ◽  
The Stability ◽  
Disease Free

ABSTRAKMakalah ini membahas dinamika transmisi COVID-19 dengan melibatkan intervensi karantina. Model dikonstruksi dengan melibatkan tiga kelas penyebab infeksi, yaitu kelas manusia terpapar, kelas manusia terinfeksi tanpa gejala klinis, dan kelas manusia terinfeksi disertai gejala klinis. Variabel yang merepresentasikan intervensi karantina untuk menekan pertumbuhan infeksi juga dipertimbangkan pada model. Selanjutnya, analisis model difokuskan pada eksistensi titik kesetimbangan dan simulasi numerik untuk menunjukkan dinamika populasi secara visual. Model yang dikonstruksi membentuk model SEAQIR yang memiliki dua titik kesetimbangan, yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik. Analisis kestabilan menunjukkan bahwa titik kesetimbangan bebas penyakit bersifat stabil asimtotik lokal pada saat R01 dan tidak stabil pada saat R01. Simulasi numerik menunjukkan bahwa peningkatan intervensi berupa karantina dapat berkontribusi memperlambat transmisi COVID-19 sehingga diharapkan dapat mencegah terjadinya wabah pada populasi.ABSTRACTThis paper discusses the dynamics of COVID-19 transmission by involving quarantine interventions. The model was constructed by involving three classes of infectious causes, namely the exposed human class, asymptotically infected human class, and symptomatic infected human class. Variables were representing quarantine interventions to suppress infection growth were also considered in the model. Furthermore, model analysis is focused on the existence of equilibrium points and numerical simulations to visually showed population dynamics. The constructed model forms the SEAQIR model which has two equilibrium points, namely a disease-free equilibrium point and an endemic equilibrium point. The stability analysis showed that the disease-free equilibrium point was locally asymptotically stable at R01 and unstable at R01. Numerical simulations showed that increasing interventions in the form of quarantine could contribute to slowing the transmission of COVID-19 so that it is hoped that it can prevent outbreaks in the population.

SYNCHRONIZATION AND GENERALIZED SYNCHRONIZATION OF FRACTIONAL ORDER CHAOTIC SYSTEMS

2009 ◽  
Vol 23 (13) ◽  
pp. 1695-1714 ◽  
Author(s):  
XING-YUAN WANG ◽  
JING ZHANG
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
State Observer ◽  
Generalized Synchronization ◽  
Fractional Order Systems ◽  
The Stability

In this paper, based on the modified state observer method, synchronization and generalized synchronization of a class of fractional order chaotic systems are presented. The two synchronization approaches are theoretically and numerically studied and two simple criterions are proposed. By using the stability theory of linear fractional order systems, suitable conditions for achieving synchronization and generalized synchronization are given. Numerical simulations coincide with the theoretical analysis.

Sign in / Sign up

Export Citation Format

Share Document