scholarly journals Synchronization for a Class of Uncertain Fractional Order Chaotic Systems with Unknown Parameters Using a Robust Adaptive Sliding Mode Controller

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Yan Yan
Keyword(s):  
Fractional Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Unknown Parameters ◽  
Adaptive Sliding Mode Controller ◽  
Mode Synchronization ◽  
Robust Adaptive

This paper deals with the synchronization of a class of fractional order chaotic systems with unknown parameters and external disturbance. Based on the Lyapunov stability theory, a fractional order sliding mode is constructed and a controller is proposed to realize chaos synchronization. The presented method not only realizes the synchronization of the considered chaotic systems but also enhances the robustness of sliding mode synchronization. Finally, some simulation results demonstrate the effectiveness and robustness of the proposed method.

Adaptive Modified Hybrid Robust Projective Synchronization Between Identical and Nonidentical Fractional-Order Complex Chaotic Systems With Fully Unknown Parameters

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Hadi Delavari ◽  
Milad Mohadeszadeh
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Order Complex ◽  
Unknown Parameters ◽  
Adaptive Sliding Mode Controller ◽  
Robust Adaptive ◽  
Complex Chaotic Systems

In this paper, a robust adaptive sliding mode controller is proposed. Under the existence of external disturbances, modified hybrid projective synchronization (MHPS) between two identical and two nonidentical fractional-order complex chaotic systems is achieved. It is shown that the response system could be synchronized with the drive system up to a nondiagonal scaling matrix. An adaptive controller and parameter update laws are investigated based on the Lyapunov stability theorem. The closed-loop stability conditions are derived based on the fractional-order Lyapunov function and Mittag-Leffler function. Finally, numerical simulations are given to verify the theoretical analysis.

scholarly journals Adaptive Synchronization for Two Different Stochastic Chaotic Systems with Unknown Parameters via a Sliding Mode Controller

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Zengyun Wang ◽  
Lihong Huang ◽  
Xuxin Yang ◽  
Dingyang Lu
Keyword(s):  
Chaotic Systems ◽  
Sliding Mode ◽  
Lyapunov Theory ◽  
Adaptive Synchronization ◽  
Sliding Mode Controller ◽  
Unknown Parameters ◽  
Adaptive Sliding Mode ◽  
Adaptive Sliding Mode Controller ◽  
Main Work ◽  
Robust Adaptive

This paper investigates the problem of synchronization for two different stochastic chaotic systems with unknown parameters and uncertain terms. The main work of this paper consists of the following aspects. Firstly, based on the Lyapunov theory in stochastic differential equations and the theory of sliding mode control, we propose a simple sliding surface and discuss the occurrence of the sliding motion. Secondly, we design an adaptive sliding mode controller to realize the asymptotical synchronization in mean squares. Thirdly, we design an adaptive sliding mode controller to realize the almost surely synchronization. Finally, the designed adaptive sliding mode controllers are used to achieve synchronization between two pairs of different stochastic chaos systems (Lorenz-Chen and Chen-Lu) in the presence of the uncertainties and unknown parameters. Numerical simulations are given to demonstrate the robustness and efficiency of the proposed robust adaptive sliding mode controller.

scholarly journals Projective synchronization of different uncertain fractional-order multiple chaotic systems with input nonlinearity via adaptive sliding mode control

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Zahra Rashidnejad Heydari ◽  
Paknosh Karimaghaee
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Adaptive Sliding Mode Control ◽  
Unknown Parameters ◽  
Input Nonlinearity ◽  
Adaptive Sliding Mode ◽  
Adaptive Sliding Mode Controller ◽  
Multiple Chaotic Systems

AbstractThis paper introduces the projective synchronization of different fractional-order multiple chaotic systems with uncertainties, disturbances, unknown parameters, and input nonlinearities. A fractional adaptive sliding surface is suggested to guarantee that more slave systems synchronize with one master system. First, an adaptive sliding mode controller is proposed for the synchronization of fractional-order multiple chaotic systems with unknown parameters and disturbances. Then, the synchronization of fractional-order multiple chaotic systems in the presence of uncertainties and input nonlinearity is obtained. The developed method can be used for many of fractional-order multiple chaotic systems. The bounds of the uncertainties and disturbances are unknown. Suitable adaptive rules are established to overcome the unknown parameters. Based on the fractional Lyapunov theorem, the stability of the suggested technique is proved. Finally, the simulation results demonstrate the feasibility and robustness of our suggested scheme.

Robust Adaptive Synchronization of Chaotic Systems With Nonsymmetric Input Saturation Constraints

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Samaneh Mohammadpour ◽  
Tahereh Binazadeh
Keyword(s):  
Chaotic Systems ◽  
Sliding Mode ◽  
Input Saturation ◽  
Adaptive Synchronization ◽  
Adaptive Sliding Mode Controller ◽  
Robust Synchronization ◽  
Effective Performance ◽  
Saturation Constraints ◽  
Robust Adaptive ◽  
Input Saturation Constraints

This paper considers the robust synchronization of chaotic systems in the presence of nonsymmetric input saturation constraints. The synchronization happens between two nonlinear master and slave systems in the face of model uncertainties and external disturbances. A new adaptive sliding mode controller is designed in a way that the robust synchronization occurs. In this regard, a theorem is proposed, and according to the Lyapunov approach the adaptation laws are derived, and it is proved that the synchronization error converges to zero despite of the uncertain terms in master and slave systems and nonsymmetric input saturation constraints. Finally, the proposed method is applied on chaotic gyro systems to show its applicability. Computer simulations verify the theoretical results and also show the effective performance of the proposed controller.

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.

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