Chaos, Sliding Mode Control between Two Different Fractional-Order Hyperchaotic Systems with Uncertain Parameters

2012 ◽  
Vol 424-425 ◽  
pp. 318-323
Author(s):  
Hong Zhang ◽  
Dao Yin Qiu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Control Method ◽  
Sliding Mode ◽  
Order System ◽  
Hyperchaotic System ◽  
Uncertain Parameters ◽  
Mode Control ◽  
Short Period ◽  
The Stability

This work investigates chaos synchronization between two different fractional-order hyperchaotic system (FOHS)s with uncertain parameters. The Chen FOHS is controlled to be synchronized with a new FOHS. The analytical conditions for the synchronization of different FOHSs are derived by utilizing the stability theory of fractional-order system. Furthermore, synchronization between two different FOHSs is achieved by utilizing sliding mode control method in a quite short period and both remain in chaotic states. Numerical simulations are used to verify the theoretical analysis using different values of the fractional-order parameter

scholarly journals Sliding Mode Control and Modified Generalized Projective Synchronization of a New Fractional-Order Chaotic System

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Junbiao Guan ◽  
Kaihua Wang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Control Technique ◽  
Order System ◽  
Mode Control ◽  
The Stability

A new fractional-order chaotic system is addressed in this paper. By applying the continuous frequency distribution theory, the indirect Lyapunov stability of this system is investigated based on sliding mode control technique. The adaptive laws are designed to guarantee the stability of the system with the uncertainty and external disturbance. Moreover, the modified generalized projection synchronization (MGPS) of the fractional-order chaotic systems is discussed based on the stability theory of fractional-order system, which may provide potential applications in secure communication. Finally, some numerical simulations are presented to show the effectiveness of the theoretical results.

scholarly journals Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

2021 ◽  
pp. 002029402110211
Author(s):  
Tao Chen ◽  
Damin Cao ◽  
Jiaxin Yuan ◽  
Hui Yang
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Tracking Error ◽  
Adaptive Neural Network ◽  
Dynamic Surface ◽  
Mode Control ◽  
The Stability

This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

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.

Robust Synchronization of Fractional-Order Arneodo Chaotic Systems Using a Fractional Sliding Mode Control Strategy

2018 ◽  
pp. 1-22
Author(s):  
Samir Ladaci ◽  
Karima Rabah ◽  
Mohamed Lashab
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Control Design ◽  
Lyapunov Stability Theory ◽  
Mode Control ◽  
Control Configuration ◽  
The Stability

This chapter investigates a new control design methodology for the synchronization of fractional-order Arneodo chaotic systems using a fractional-order sliding mode control configuration. This class of nonlinear fractional-order systems shows a chaotic behavior for a set of model parameters. The stability analysis of the proposed fractional-order sliding mode control law is performed by means of the Lyapunov stability theory. Simulation examples on fractional-order Arneodo chaotic systems synchronization are provided in presence of disturbances and noises. These results illustrate the effectiveness and robustness of this control design approach.

Fixed-time fractional-order sliding mode control for nonlinear power systems

2020 ◽  
Vol 26 (17-18) ◽  
pp. 1425-1434 ◽  
Author(s):  
Sunhua Huang ◽  
Jie Wang
Keyword(s):  
Sliding Mode Control ◽  
Power System ◽  
Fractional Order ◽  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
Fixed Time ◽  
Sliding Mode Controller ◽  
Mode Control ◽  
Time Control

In this study, a fractional-order sliding mode controller is effectively proposed to stabilize a nonlinear power system in a fixed time. State trajectories of a nonlinear power system show nonlinear behaviors on the angle and frequency of the generator, phase angle, and magnitude of the load voltage, which would seriously affect the safe and stable operation of the power grid. Therefore, fractional calculus is applied to design a fractional-order sliding mode controller which can effectively suppress the inherent chattering phenomenon in sliding mode control to make the nonlinear power system converge to the equilibrium point in a fixed time based on the fixed-time stability theory. Compared with the finite-time control method, the convergence time of the proposed fixed-time fractional-order sliding mode controller is not dependent on the initial conditions and can be exactly evaluated, thus overcoming the shortcomings of the finite-time control method. Finally, superior performances of the fractional-order sliding mode controller are effectively verified by comparing with the existing finite-time control methods and integral order sliding mode control through numerical simulations.

Variable fractional order sliding mode control for seismic vibration suppression of building structure

2021 ◽  
pp. 107754632110396
Author(s):  
Chunxiu Wang ◽  
Xingde Zhou ◽  
Yitong Jin ◽  
Xianzeng Shi
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Vibration Suppression ◽  
Control Method ◽  
Sliding Mode ◽  
Building Structure ◽  
Seismic Excitations ◽  
Mode Control ◽  
Fractional Order Controller ◽  
Control Output

Constant fractional order vibration control strategy has been one of research hotspots in recent decades. However, the variable fractional order control method is seldom concerned up to now. In this article, a novel variable fractional order sliding mode control (VOSMC) method is proposed to suppress the responses of building structure caused by seismic excitations, including El Centro, Hachinohe, Northridge, and Kobe earthquakes. Based on the proposed variable fractional order sliding mode surface, the control law of VOSMC is presented. The global asymptotic stability of the control system is analyzed and proved by utilizing variable fractional order Lyapunov stability theorem. Besides, the corresponding constant fractional order sliding mode control (COSMC) method is also given. The control effects of VOSMC and COSMC methods are discussed by four performance indices. Finally, the utilizability and reasonability of the proposed control method is verified by using two examples (include two-story and five-story shear buildings). Compared with the COSMC method, the proposed variable fractional order controller not only has a lesser control output, but also has a higher utilization of the output, which is conducive to energy saving.

Synchronization of Fractional-Order Chaotic Systems with Uncertain Parameters

2010 ◽  
Vol 171-172 ◽  
pp. 723-727
Author(s):  
Hong Zhang ◽  
Qiu Mei Pu
Keyword(s):  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
System Stability ◽  
Order System ◽  
Uncertain Parameters ◽  
Mode Theory ◽  
Simulation Results ◽  
The Stability

For the synchronization of fractional-order chaotic systems with uncertain parameters, a controller based on sliding mode theory is presented. Based on the stability theory of fractional-order system, stability of the proposed method is analyzed. The theory is successfully applied to synchronize fractional Newton-Leipnik chaotic systems with uncertain parameters. The simulation results show the effectiveness of the proposed controller.

scholarly journals Adaptive Fractional Fuzzy Sliding Mode Control for Multivariable Nonlinear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Junhai Luo ◽  
Heng Liu
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Control Method ◽  
Sliding Mode ◽  
Fuzzy Sliding Mode Control ◽  
Integer Order ◽  
Mode Control ◽  
Fuzzy Sliding Mode ◽  
Multivariable Nonlinear Systems

This paper presents a robust adaptive fuzzy sliding mode control method for a class of uncertain nonlinear systems. The fractional order calculus is employed in the parameter updating stage. The underlying stability analysis as well as parameter update law design is carried out by Lyapunov based technique. In the simulation, two examples including a comparison with the traditional integer order counterpart are given to show the effectiveness of the proposed method. The main contribution of this paper consists in the control performance is better for the fractional order updating law than that of traditional integer order.

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