scholarly journals Adaptive Sliding Control for a Class of Fractional Commensurate Order Chaotic Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Jian Yuan ◽  
Bao Shi ◽  
Zhentao Yu
Keyword(s):  
Chaotic Systems ◽  
Sliding Mode ◽  
Adaptive Sliding Mode Control ◽  
External Disturbances ◽  
Fractional Systems ◽  
Sliding Control ◽  
Sliding Manifold ◽  
The Stability ◽  
Adaptation Law ◽  
Sliding Dynamics

This paper proposes adaptive sliding mode control design for a class of fractional commensurate order chaotic systems. We firstly introduce a fractional integral sliding manifold for the nominal systems. Secondly we prove the stability of the corresponding fractional sliding dynamics. Then, by introducing a Lyapunov candidate function and using the Mittag-Leffler stability theory we derive the desired sliding control law. Furthermore, we prove that the proposed sliding manifold is also adapted for the fractional systems in the presence of uncertainties and external disturbances. At last, we design a fractional adaptation law for the perturbed fractional systems. To verify the viability and efficiency of the proposed fractional controllers, numerical simulations of fractional Lorenz’s system and Chen’s system are presented.

Another Note on Stability of Sliding Mode Dynamics in Suppression of Fractional Chaotic Systems

2015 ◽  
Vol 743 ◽  
pp. 303-306
Author(s):  
J. Yuan ◽  
B. Shi ◽  
Yan Wang
Keyword(s):  
Stability Analysis ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Fractional Systems ◽  
Infinite Dimensional ◽  
Fractional Integrator ◽  
Fractional Differential ◽  
Continuous Frequency ◽  
The Stability ◽  
Sliding Mode Dynamics

This paper revisits the stability analysis of sliding mode dynamics in suppression of a classof fractional chaotic systems by a different approach. Firstly, we convert fractional differential equationsinto infinite dimensional ordinary differential equations based on the continuous frequency distributedmodel of the fractional integrator. Then we choose a Lyapunov function candidate to proposethe stability analysis. The result applies to both the commensurate fractional systems and the incommensurateones.

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.

scholarly journals Adaptive Sliding Mode Control Vibrations of Structures

2021 ◽  
Author(s):  
Fali Leyla ◽  
Zizouni Khaled ◽  
Saidi Abdelkrim ◽  
Bousserhane Ismail Khalil ◽  
Djermane Mohamed
Keyword(s):  
Controller Design ◽  
Sliding Mode ◽  
Adaptive Controller ◽  
Structural Vibration ◽  
Adaptive Sliding Mode Control ◽  
Sliding Mode Controller ◽  
Active Devices ◽  
The Stability ◽  
Adaptation Law ◽  
Low Sensitivity

The sliding mode controller is one of the interesting classical nonlinear controllers in structural vibration control. From its apparition, in the middle of the twentieth century, this controller was a subject of several studies and investigations. This controller was widely used in the control of various semi-active or active devices in the civil engineering area. Nevertheless, the sliding mode controller offered a low sensitivity to the uncertainties or the system condition variations despite the presence of the Chattering defect. However, the adaptation law is one of the frequently used solutions to overcome this phenomenon offering the possibility to adapt the controller parameters according to the system variations and keeping the stability of the whole system assured. The chapter provides a sliding mode controller design reinforced by an adaptive law to control the desired state of an excited system. The performance of the adaptive controller is proved by numerical simulation results of a three-story excited structure.

Adaptive Sliding Mode Spacecraft Attitude Control

2014 ◽  
Author(s):  
Yizhou Wang ◽  
Xu Chen ◽  
Masayoshi Tomizuka
Keyword(s):  
Attitude Control ◽  
Sliding Mode ◽  
Spacecraft Attitude ◽  
Control Analysis ◽  
External Disturbances ◽  
Parameter Adaptation ◽  
Adaptive Sliding Mode ◽  
Sliding Manifold ◽  
Adaptation Law ◽  
Velocity Tracking

An adaptive sliding mode spacecraft attitude controller is derived in this paper. It has the advantage of not requiring knowledge of the inertia of the spacecraft, and rejecting unexpected external disturbances, with global asymptotic position and velocity tracking. The sliding manifold is designed using optimal control analysis of the quaternion kinematics. The sliding mode control law and the parameter adaptation law are designed using Lyapunov stability. Numerical simulations are performed to demonstrate both the nominal and the robust performance.

scholarly journals Synchronization of Non-Integer Complex Chaotic Systems with Uncertainty and Disturbances via Adaptive Sliding Mode Technique

2020 ◽  
Vol 12 (2) ◽  
pp. 189-200 ◽  
Author(s):  
L. S. Jahanzaib ◽  
P. Trikha ◽  
Nasreen
Keyword(s):  
Chaotic Systems ◽  
Sliding Mode ◽  
Control Technique ◽  
Adaptive Sliding Mode Control ◽  
Control Law ◽  
External Disturbances ◽  
Adaptive Sliding Mode ◽  
Complex Chaotic Systems ◽  
Mode Technique ◽  
Sliding Mode Technique

In this paper we concern the adaptive sliding mode control technique for synchronization of fractional order chaotic systems with uncertainties and disturbances. This technique is used to design control law through suitable sliding surface and estimate the external disturbances. Computational results using MATLAB verified the effectiveness of the proposed scheme.

scholarly journals Sliding Mode Control of the Fractional-Order Unified Chaotic System

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Jian Yuan ◽  
Bao Shi ◽  
Xiaoyun Zeng ◽  
Wenqiang Ji ◽  
Tetie Pan
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Adaptive Sliding Mode Control ◽  
External Disturbances ◽  
Mode Control ◽  
Unified Chaotic System ◽  
Unified Chaotic Systems ◽  
Systematic Uncertainties

This paper deals with robust synchronization of the fractional-order unified chaotic systems. Firstly, control design for synchronization of nominal systems is proposed via fractional sliding mode technique. Then, systematic uncertainties and external disturbances are considered in the fractional-order unified chaotic systems, and adaptive sliding mode control is designed for the synchronization issue. Finally, numerical simulations are carried out to verify the effectiveness of the two proposed control techniques.

Control of Fractional-Order Systems Using Chatter-Free Sliding Mode Approach

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Mohammad Pourmahmood Aghababa
Keyword(s):  
Fractional Derivative ◽  
Sliding Mode ◽  
Variable Structure ◽  
Stability And Convergence ◽  
Control Input ◽  
Fractional Systems ◽  
Sliding Motion ◽  
Efficient Performance ◽  
Sliding Manifold ◽  
Chattering Free

The problem of stabilization of nonlinear fractional systems in spite of system uncertainties is investigated in this paper. First, a proper fractional derivative type sliding manifold with desired stability and convergence properties is designed. Then, the fractional stability theory is adopted to derive a robust sliding control law to force the system trajectories to attain the proposed sliding manifold and remain on it evermore. The existence of the sliding motion is mathematically proven. Furthermore, the sign function in the control input, which is responsible to the being of harmful chattering, is transferred into the fractional derivative of the control input. Therefore, the resulted control input becomes smooth and free of the chattering. Some numerical simulations are presented to illustrate the efficient performance of the proposed chattering-free fractional variable structure controller.

scholarly journals Active Sliding Mode for Synchronization of a Wide Class of Four-Dimensional Fractional-Order Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Wang ◽  
Yuangui Zhou ◽  
Jianyi Xue ◽  
Delan Zhu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Wide Class ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Order System ◽  
Fractional Order Calculus ◽  
Simulation Results ◽  
The Stability

We focus on the synchronization of a wide class of four-dimensional (4-D) chaotic systems. Firstly, based on the stability theory in fractional-order calculus and sliding mode control, a new method is derived to make the synchronization of a wide class of fractional-order chaotic systems. Furthermore, the method guarantees the synchronization between an integer-order system and a fraction-order system and the synchronization between two fractional-order chaotic systems with different orders. Finally, three examples are presented to illustrate the effectiveness of the proposed scheme and simulation results are given to demonstrate the effectiveness of the proposed method.

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