scholarly journals Robust Synchronization Control of Uncertain Fractional-Order Chaotic Systems via Disturbance Observer

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Kaijuan Xue ◽  
Yongbing Huangfu
Keyword(s):  
Fractional Order ◽  
Disturbance Observer ◽  
Chaotic Systems ◽  
Control Method ◽  
Observer Design ◽  
Synchronization Error ◽  
Synchronization Control ◽  
Compact Set ◽  
Control Scheme ◽  
Unknown Disturbances

This paper studies the synchronization of two different fractional-order chaotic systems through the fractional-order control method, which can ensure that the synchronization error converges to a sufficiently small compact set. Afterwards, the disturbance observer of the synchronization control scheme based on adaptive parameters is designed to predict unknown disturbances. The Lyapunov function method is used to verify the appropriateness of the disturbance observer design and the convergence of the synchronization error, and then the feasibility of the control scheme is obtained. Finally, our simulation studies verify and clarify the proposed method.

Sliding-Mode Disturbance Observer-Based Control for Fractional-Order System with Unknown Disturbances

2020 ◽  
Vol 08 (03) ◽  
pp. 193-202
Author(s):  
Yuanlong Xie ◽  
Xiaolong Zhang ◽  
Liquan Jiang ◽  
Jie Meng ◽  
Gen Li ◽  
...  
Keyword(s):  
Fractional Order ◽  
Disturbance Observer ◽  
Control Method ◽  
Sliding Mode ◽  
Dynamic Control ◽  
Order System ◽  
Fractional Order Systems ◽  
Sliding Mode Disturbance Observer ◽  
Control Scheme ◽  
Unknown Disturbances

This paper concentrates on the disturbances estimation and attenuation problem of a general class of the fractional-order systems. For this purpose, this paper proposes a fractional sliding-mode disturbance observer (FSMDO)-based control scheme, which is capable of mitigating the unknown disturbances asymptotically. Meanwhile, by incorporating a novel fractional sliding-mode controller into the proposed control scheme, the asymptotical convergence of trajectory tracking errors is guaranteed. The developed control scheme owns three attractive highlights: (1) it is suitable for the general fractional-order systems, including nonlinear systems and incommensurate systems; (2) the proposed FSMDO can estimate the unknown exogenous disturbances and system uncertainties timely and precisely; (3) nominal performance can be retained by compensating the observed disturbances in a feedforward manner, and thus, the robustness of the system can be strengthened. Illustrative examples are provided to show the availability and superiority of the presented FSMDO control method in terms of robust control. As compared with the conventional methods, the dynamic control performance of the closed-loop system can be improved.

scholarly journals A Robust Control Method forQ-SSynchronization between Different Dimensional Integer-Order and Fractional-Order Chaotic Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Adel Ouannas ◽  
Raghib Abu-Saris
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Control Approach ◽  
Integer Order ◽  
Control Scheme ◽  
Master System ◽  
Different Dimensions ◽  
Hyperchaotic Systems

A robust control approach is presented to study the problem ofQ-Ssynchronization between Integer-order and fractional-order chaotic systems with different dimensions. Based on Laplace transformation and stability theory of linear integer-order dynamical systems, a new control law is proposed to guarantee theQ-Ssynchronization betweenn-dimensional integer-order master system andm-dimensional fractional-order slave system. This paper provides further contribution to the topic ofQ-Schaos synchronization between integer-order and fractional-order systems and introduces a general control scheme that can be applied to wide classes of chaotic and hyperchaotic systems. Illustrative example and numerical simulations are used to show the effectiveness of the proposed method.

A computationally efficient adaptive robust control scheme for a quad-rotor transporting cable-suspended payloads

2021 ◽  
pp. 095441002110136
Author(s):  
Nasim Ullah ◽  
Irfan Sami ◽  
Wang Shaoping ◽  
Hamid Mukhtar ◽  
Xingjian Wang ◽  
...  
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Adaptive Robust Control ◽  
Computationally Efficient ◽  
Control Scheme ◽  
Control Schemes ◽  
Adaptive Laws ◽  
Unknown Disturbances ◽  
The Stability

This article proposes a computationally efficient adaptive robust control scheme for a quad-rotor with cable-suspended payloads. Motion of payload introduces unknown disturbances that affect the performance of the quad-rotor controlled with conventional schemes, thus novel adaptive robust controllers with both integer- and fractional-order dynamics are proposed for the trajectory tracking of quad-rotor with cable-suspended payload. The disturbances acting on quad-rotor due to the payload motion are estimated by utilizing adaptive laws derived from integer- and fractional-order Lyapunov functions. The stability of the proposed control systems is guaranteed using integer- and fractional-order Lyapunov theorems. Overall, three variants of the control schemes, namely adaptive fractional-order sliding mode (AFSMC), adaptive sliding mode (ASMC), and classical Sliding mode controllers (SMC)s) are tested using processor in the loop experiments, and based on the two performance indicators, namely robustness and computational resource utilization, the best control scheme is evaluated. From the results presented, it is verified that ASMC scheme exhibits comparable robustness as of SMC and AFSMC, while it utilizes less sources as compared to AFSMC.

Comparison of Times of Synchronization of Chaotic Burke-Shaw Attractor with Active Control and Integer and Optimum Fractional-Order Pecaro Carroll Method

2021 ◽  
Author(s):  
Ali Durdu ◽  
Yılmaz Uyaroğlu
Keyword(s):  
Active Control ◽  
Fractional Order ◽  
Chaotic Attractor ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Control Method ◽  
Initial Conditions ◽  
Data Communication ◽  
Experimental Results ◽  
Active Control Method

Abstract Many studies have been introduced in the literature showing that two identical chaotic systems can be synchronized with different initial conditions. Secure data communication applications have also been made using synchronization methods. In the study, synchronization times of two popular synchronization methods are compared, which is an important issue for communication. Among the synchronization methods, active control, integer, and fractional-order Pecaro Carroll (P-C) method was used to synchronize the Burke-Shaw chaotic attractor. The experimental results showed that the P-C method with optimum fractional-order is synchronized in 2.35 times shorter time than the active control method. This shows that the P-C method using fractional-order creates less delay in synchronization and is more convenient to use in secure communication applications.

Projective synchronization via adaptive pinning control for fractional-order complex network with time-varying coupling strength

2019 ◽  
Vol 30 (07) ◽  
pp. 1940013
Author(s):  
Darui Zhu ◽  
Rui Wang ◽  
Chongxin Liu ◽  
Jiandong Duan
Keyword(s):  
Complex Network ◽  
Fractional Order ◽  
Control Method ◽  
Pinning Control ◽  
Projective Synchronization ◽  
Synchronization Control ◽  
Order Complex ◽  
Selection Algorithm ◽  
Feedback Control Method ◽  
Simulation Results

This paper presents an adaptive projective pinning control method for fractional-order complex network. First, based on theories of complex network and fractional calculus, some preliminaries of mathematics are given. Then, an analysis is conducted on the adaptive projective pinning control theory for fractional-order complex network. Based on the projective synchronization control method and the combined adaptive pinning feedback control method, suitable projection synchronization scale factor, adaptive feedback controller and the node selection algorithm are designed to illustrate the synchronization for fractional-order hyperchaotic complex network. Simulation results show that all nodes are stabilized to equilibrium point. Theoretical analysis and simulation results demonstrate that the designed adaptive projective pinning controllers are efficient.

Terminal observer and disturbance observer for the class of fractional-order chaotic systems

2019 ◽  
Vol 24 (12) ◽  
pp. 8881-8898
Author(s):  
Mohammad Reza Soltanpour ◽  
Mehrdad Shirkavand
Keyword(s):  
Fractional Order ◽  
Disturbance Observer ◽  
Chaotic Systems

scholarly journals Control Scheme for a Fractional-Order Chaotic Genesio-Tesi Model

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Changjin Xu ◽  
Peiluan Li ◽  
Maoxin Liao ◽  
Zixin Liu ◽  
Qimei Xiao ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Characteristic Equation ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Feedback Controllers ◽  
Control Scheme ◽  
The Stability ◽  
Time Delayed Feedback

In this paper, based on the earlier research, a new fractional-order chaotic Genesio-Tesi model is established. The chaotic phenomenon of the fractional-order chaotic Genesio-Tesi model is controlled by designing two suitable time-delayed feedback controllers. With the aid of Laplace transform, we obtain the characteristic equation of the controlled chaotic Genesio-Tesi model. Then by regarding the time delay as the bifurcation parameter and analyzing the characteristic equation, some new sufficient criteria to guarantee the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model are derived. The research shows that when time delay remains in some interval, the equilibrium point of the controlled chaotic Genesio-Tesi model is stable and a Hopf bifurcation will happen when the time delay crosses a critical value. The effect of the time delay on the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model is shown. At last, computer simulations check the rationalization of the obtained theoretical prediction. The derived key results in this paper play an important role in controlling the chaotic behavior of many other differential chaotic systems.

The Model of Liu Chaotic Synchronization with Oscillating Parameters under the Impulsive Control

2011 ◽  
Vol 480-481 ◽  
pp. 1378-1382
Author(s):  
Yan Hui Chen
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Chaotic Synchronization ◽  
Control Signal ◽  
Synchronization Control ◽  
Security Risks ◽  
Control Scheme

The control of chaotic synchronization is the kernel technology in chaos-based secure communication. Those control methods have to transmitting control signal which increase the security risks of the communication system. Attacker can reconstruct the chaotic system or estimate parameters by using the information of the chaotic system. In this paper we propose a hybrid Liu chaotic synchronization control scheme which contains both continuous chaotic system with oscillating parameters approach to 0 and discrete chaotic system. By theory of impulsive differential equations, we proved a theorem that two continuous Liu chaotic systems can get synchronized without control signal transmitting which has reduced the risk of the security.

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