Robust synchronization of two different fractional-order chaotic systems with unknown parameters using adaptive sliding mode approach

2012 ◽  
Vol 71 (1-2) ◽  
pp. 269-278 ◽  
Author(s):  
Ruoxun Zhang ◽  
Shiping Yang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Unknown Parameters ◽  
Adaptive Sliding Mode ◽  
Robust Synchronization

scholarly journals Robust Synchronization of Fractional-Order Uncertain Chaotic Systems Based on Output Feedback Sliding Mode Control

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 599 ◽  
Author(s):  
Chao Song ◽  
Shumin Fei ◽  
Jinde Cao ◽  
Chuangxia Huang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Control Technique ◽  
Unknown Parameters ◽  
Mode Control ◽  
Robust Synchronization ◽  
The Stability ◽  
Output Information

This paper mainly focuses on the robust synchronization issue for drive-response fractional-order chaotic systems (FOCS) when they have unknown parameters and external disturbances. In order to achieve the goal, the sliding mode control scheme only using output information is designed, and at the same time, the structures of a sliding mode surface and a sliding mode controller are also constructed. A sufficient criterion is presented to ensure the robust synchronization of FOCS according to the stability theory of the fractional calculus and sliding mode control technique. In addition, the result can be applied to identical or non-identical chaotic systems with fractional-order. In the end, we build two practical examples to illustrate the feasibility of our theoretical results.

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.

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