Adaptive Synchronization of a Stochastic Fractional-Order System

2015 ◽  
Vol 733 ◽  
pp. 939-942
Author(s):  
Xiao Jun Liu
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stochastic System ◽  
Fractional Order System ◽  
Adaptive Synchronization ◽  
Order System ◽  
Unknown Parameters ◽  
Adaptive Laws

In this paper, adaptive synchronization of a stochastic fractional-order system with unknown parameters is studied. Firstly, the stochastic system is reduced into the equivalent deterministic one with Laguerre approximation. Then, the synchronization for the system is realized by designing appropriate controllers and adaptive laws of the unknown parameters. Numerical simulations are carried out to demonstrate the effectiveness of the controllers and laws.

Synchronization of a Fractional-Order System with Unknown Parameters

2013 ◽  
Vol 850-851 ◽  
pp. 796-799
Author(s):  
Xiao Ya Yang
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Attractor ◽  
Fractional Order System ◽  
Order System ◽  
Fractional Order Systems ◽  
Unknown Parameters ◽  
The Stability

In this paper, synchronization of a fractional-order system with unknown parameters is studied. The chaotic attractor of the system is got by means of numerical simulation. Then based on the stability theory of fractional-order systems, suitable synchronization controllers and parameter identification rules for the unknown parameters are designed. Numerical simulations are used to demonstrate the effectiveness of the controllers.

Chaotic Dynamics of Fractional-Order Liu System

2011 ◽  
Vol 55-57 ◽  
pp. 1327-1331 ◽  
Author(s):  
Xin Gao
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic Dynamics ◽  
Fractional Order System ◽  
Order System ◽  
Liu System

In this paper, we numerically investigate the chaotic behaviors of a new fractional-order system. We find that chaotic behaviors exist in the fractional-order system with order less than 3. The lowest order we find to have chaos is 2.4 in such system. In addition, we numerically simulate the continuances of the chaotic behaviors in the fractional-order system with orders from 2.7 to 3. Our investigations are validated through numerical simulations.

The Synchronization of a Fractional-Order Chaotic System

2013 ◽  
Vol 655-657 ◽  
pp. 1488-1491
Author(s):  
Fan Di Zhang
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic System ◽  
Stability Theory ◽  
Fractional Order System ◽  
Order System ◽  
Integer Order

In this paper, the synchronization of fractional-orderchaotic system is studied. Based on the fractional stability theory, suitable controller is designed to realize the synchronization between fractional-order system and a integer-order system. Numerical simulations show that the effectiveness and feasibility of the controllers .

scholarly journals Adaptive synchronization of a class of fractional order chaotic system with uncertain parameters

2015 ◽  
Vol 11 (6) ◽  
pp. 5306-5316
Author(s):  
De-fu Kong
Keyword(s):  
Parameter Identification ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic System ◽  
Stability Criterion ◽  
Local Stability ◽  
Adaptive Synchronization ◽  
Uncertain Parameters ◽  
Unknown Parameters ◽  
Control Scheme

In this manuscript, the adaptive synchronization of a class of fractional order chaotic system with uncertain parameters is studied. Firstly, the local stability of the fractional order chaotic system is analyzed using fractional stability criterion. Then, based on the J function criterion, suitable adaptive synchronization controller and parameter identification rules of the unknown parameters are investigated. Finally, the numerical simulations are presented to verify the effectiveness and robustness of the proposed control scheme.

scholarly journals Adaptive Stabilization of a Fractional-Order System with Unknown Disturbance and Nonlinear Input via a Backstepping Control Technique

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 55
Author(s):  
Xiaomin Tian ◽  
Zhong Yang
Keyword(s):  
Fractional Order ◽  
Dead Zone ◽  
External Disturbance ◽  
Lyapunov Theory ◽  
Fractional Order System ◽  
Control Technique ◽  
Order System ◽  
Distributed Model ◽  
Adaptive Stabilization ◽  
Unknown Parameters

In this paper, a new backstepping-based adaptive stabilization of a fractional-order system with unknown parameters is investigated. We assume that the controlled system is perturbed by external disturbance, the bound of external disturbance to be unknown in advance. Moreover, the effects of sector and dead-zone nonlinear inputs both are taken into account. A fractional-order auxiliary system is established to generate the necessary signals for compensation the nonlinear inputs. Meantime, in order to deal with these unknown parameters, some fractional-order adaption laws are given. The frequency-distributed model is used so that the indirect Lyapunov theory is available in designing controllers. Finally, simulation results are presented to verify the effectiveness and robustness of the proposed control strategy.

Adaptive Synchronization of a Fractional-Order Complex T System With a Random Parameter

2015 ◽  
Author(s):  
Xiaojun Liu ◽  
Ling Hong
Keyword(s):  
Fractional Order ◽  
Laguerre Polynomial ◽  
Random Parameter ◽  
Adaptive Synchronization ◽  
Order System ◽  
Deterministic System ◽  
Order Complex ◽  
Unknown Parameters ◽  
The Stability ◽  
T System

In this paper, the adaptive synchronization of a fractional-order complex T system with a random parameter is analyzed. Firstly, the Laguerre polynomial approximation method is applied to investigate the fractional-order system with a random parameter which obeys an exponential distribution. Based on this method, the stochastic system is reduced into the equivalent deterministic one. The improved Adams-Bashforth-Moulton algorithm with the predictor-correctors scheme is used to solve the approximately deterministic system numerically. Based on the stability theory of fractional-order systems, the synchronization for the deterministic system with unknown parameters is realized by designing appropriate synchronization controllers and estimation law for uncertain parameters. Numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed scheme.

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