Using Active Sliding Mode Controller Antisynchronization of Fractional-Order Chaotic Systems with Uncertainties and Disturbances

2013 ◽  
Vol 411-414 ◽  
pp. 1779-1786
Author(s):  
Hong Zhang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
External Disturbances ◽  
Active Sliding Mode Control ◽  
Derivative Method ◽  
Method Analysis

The antisynchronization behavior of fractional-order chaotic systems with parametric uncertainties and external disturbances is explored by using robust active sliding mode control method. The sufficient conditions for achieving robust antisynchronization of two identical fractional-order chaotic systems with different initial conditions and two different fractional-order chaotic systems with terms of uncertainties and external disturbances are derived based on the fractional-order derivative method. Analysis and numerical simulations are shown for validation purposes.

scholarly journals Active Sliding Mode Control Antisynchronization of Chaotic Systems with Uncertainties and External Disturbances

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Wafaa Jawaada ◽  
M. S. M. Noorani ◽  
M. Mossa Al-sawalha
Keyword(s):  
Sliding Mode Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
External Disturbances ◽  
Mode Control ◽  
Active Sliding Mode Control

The antisynchronization behavior of chaotic systems with parametric uncertainties and external disturbances is explored by using robust active sliding mode control method. The sufficient conditions for achieving robust antisynchronization of two identical chaotic systems with different initial conditions and two different chaotic systems with terms of uncertainties and external disturbances are derived based on the Lyapunov stability theory. Analysis and numerical simulations are shown for validation purposes.

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.

scholarly journals The Robust Control and Synchronization of a Class of Fractional-Order Chaotic Systems with External Disturbances via a Single Output

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Runzi Luo ◽  
Haipeng Su
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
External Disturbances ◽  
Numerical Examples ◽  
Single Output ◽  
Lorenz Chaotic System ◽  
Control And Synchronization

This paper investigates the stabilization and synchronization of a class of fractional-order chaotic systems which are affected by external disturbances. The chaotic systems are assumed that only a single output can be used to design the controller. In order to design the proper controller, some observer systems are proposed. By using the observer systems some sufficient conditions for achieving chaos control and synchronization of fractional-order chaotic systems are derived. Numerical examples are presented by taking the fractional-order generalized Lorenz chaotic system as an example to show the feasibility and validity of the proposed method.

scholarly journals Robust Synchronization of Incommensurate Fractional-Order Chaotic Systems via Second-Order Sliding Mode Technique

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Hua Chen ◽  
Wen Chen ◽  
Binwu Zhang ◽  
Haitao Cao
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Controller Design ◽  
Sliding Mode ◽  
Second Order ◽  
External Disturbances ◽  
Globally Asymptotically Stable ◽  
Control Scheme ◽  
Chattering Free ◽  
Second Order Sliding Mode

A second-order sliding mode (SOSM) controller is proposed to synchronize a class of incommensurate fractional-order chaotic systems with model uncertainties and external disturbances. Based on the chattering free SOSM control scheme, it can be rigorously proved that the dynamics of the synchronization error is globally asymptotically stable by using the Lyapunov stability theorem. Finally, numerical examples are provided to illustrate the effectiveness of the proposed controller design approach.

scholarly journals Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Chenhui Wang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Synchronization Error ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
Numerical Examples ◽  
Mode Synchronization ◽  
Fractional Order Integral

Some sufficient conditions, which are valid for stability check of fractional-order nonlinear systems, are given in this paper. Based on these results, the synchronization of two fractional-order chaotic systems is investigated. A novel fractional-order sliding surface, which is composed of a synchronization error and its fractional-order integral, is introduced. The asymptotical stability of the synchronization error dynamical system can be guaranteed by the proposed fractional-order sliding mode controller. Finally, two numerical examples are given to show the feasibility of the proposed methods.

scholarly journals CentrifugationSynchronization Control of Fractional Order Chaotic Systems Based on Memristor and Its Hardware Implementation

2021 ◽  
pp. 289-297
Author(s):  
Zhaohan zhang, Huiling Jin
Keyword(s):  
Fractional Order ◽  
Hardware Implementation ◽  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Controlled System ◽  
Integer Order ◽  
The Stability ◽  
Dynamic Phenomena

This paper studies the synchronization control of fractional order chaotic systems based on memristor and its hardware implementation. This paper takes the complex dynamic phenomena of memristor turbidity system as the research background. Starting with the integer order memristor system, the fractional order form is derived based on the integer order turbid system, and its dynamics is deeply studied. At the same time, the turbidity phenomenon is applied to the watermark encryption algorithm, which effectively improves the confidentiality of the algorithm. Finally, in order to suppress the occurrence of turbidity, a fractional order sliding mode controller is proposed. In this paper, the sliding mode controller under the function switching control method is established, and the conditions for the parameters of the sliding mode controller are derived. Finally, the experimental results analyze the stability of the controlled system under different parameters, and give the corresponding time-domain waveform to verify the correctness of the theoretical analysis.

scholarly journals A non-integer sliding mode controller to stabilize fractional-order nonlinear systems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ahmadreza Haghighi ◽  
Roveida Ziaratban
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Controller Design ◽  
Nonlinear Dynamical Systems ◽  
Sliding Mode ◽  
Slip Surface ◽  
Direct Method ◽  
Distributed Model ◽  
Sliding Mode Controller

Abstract In this study, we examine the stabilization of fractional-order chaotic nonlinear dynamical systems with model uncertainties and external disturbances. We used the sliding mode controller by a new approach for controlling and stabilization of these systems. In this research, we replaced a continuous function with the sign function in the controller design and the sliding surface to suppress chattering and undesirable vibration effects. The advantages of the proposed control method are rapid convergence to the equilibrium point, the absence of chattering and unwanted oscillations, high resistance to uncertainties, and the possibility of applying this method to most fractional order chaotic systems. We applied the direct method of Lyapunov stability theory and the frequency distributed model to prove the stability of the slip surface and closed loop system. Finally, we simulated this method on two commonly used and practical chaotic systems and presented the results.

scholarly journals Linear Control of Fractional-Order Financial Chaotic Systems with Input Saturation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Junhai Luo ◽  
Guanjun Li ◽  
Heng Liu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Input Saturation ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Control ◽  
Control Input ◽  
Saturated Control ◽  
Laplace Transform Technique

In this paper, control of fractional-order financial chaotic systems with saturated control input is investigated by means of state-feedback control method. The saturation problem is tackled by using Gronwall-Bellman lemma and a memoryless nonlinearity function. Based on Gronwall inequality and Laplace transform technique, two sufficient conditions are achieved for the asymptotical stability of the fractional-order financial chaotic systems with fractional orders 0 <α≤ 1 and 1 <α< 2, respectively. Finally, simulation studies are carried out to show the effectiveness of the proposed linear control method.

Stabilization of a Class of Fractional-Order Chaotic Systems via Direct Adaptive Fuzzy Optimal Sliding Mode Control

2018 ◽  
pp. 289-304
Author(s):  
Bachir Bourouba
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Optimization Technique ◽  
External Disturbances ◽  
Control Approach ◽  
Adaptive Fuzzy ◽  
Mode Control ◽  
Fuzzy Control Strategy

In this chapter a new direct adaptive fuzzy optimal sliding mode control approach is proposed for the stabilization of fractional chaotic systems with different initial conditions of the state under the presence of uncertainties and external disturbances. Using Lyapunov analysis, the direct adaptive fuzzy optimal sliding mode control approach illustrates asymptotic convergence of error to zero as well as good robustness against external disturbances and uncertainties. The authors present a method for optimum tuning of sliding mode control system parameter using particle swarm optimization (PSO) algorithm. PSO is a robust stochastic optimization technique based on the movement and intelligence of swarm, applying the concept of social interaction to problem solving. Simulation examples for the control of nonlinear fractional-order systems are given to illustrate the effectiveness of the proposed fractional adaptive fuzzy control strategy.

scholarly journals Robust Synchronisation of Uncertain Fractional-Order Chaotic Unified Systems

2017 ◽  
Vol 71 (1-2) ◽  
pp. 69-77
Author(s):  
Naeimadeen Noghredani ◽  
Saeed Balochian
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Financial Systems ◽  
External Disturbances ◽  
Sliding Mode Controllers ◽  
Error Dynamic ◽  
Error Dynamics ◽  
Integral Sliding Surface ◽  
The Stability

Abstract Fractional-order chaotic unified systems include a variety of fractional-order chaotic systems such as Chen, Lorenz, Lu, Liu, and financial systems. This paper describes a sliding mode controller for synchronisation of fractional-order chaotic unified systems in the presence of uncertainties and external disturbances, and affirms the stability of the controller (which is composed of error dynamics). Moreover, the synchronisation of two separate fractional-order chaotic systems is studied. For this aim, fractional integral sliding surface is defined. Then the sliding mode control rule for stability of error dynamic is presented based on the Lyapunov stability theorem. Simulation results, obtained by using MATLAB, show that the proposed sliding mode has employed an appropriate approach against uncertainties and to reduce the chattering phenomenon that often occurs with sliding mode controllers.

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