Robust Control of a Class of Uncertain Fractional-Order Chaotic Systems with Input Nonlinearity via an Adaptive Sliding Mode Technique

This paper investigates the robust control problem of the uncertain unified chaotic systems subject to sector input nonlinearity. First, the adaptive parameter is introduced for designing sliding surface such that the parameters of the unified chaotic system are not necessary to know. Then, based on Lyapunov theory, the controller is designed via sliding mode technique, which cancels the assumption that the information on the bound of input nonlinearity should be known for designer in advance. Finally, the sliding mode controller is applied to ensure that different uncertain chaotic systems (Lorenz system, Lü system and Chen system) states can be regulated to zero levels asymptotically in the presence of sector input nonlinearity. The simulation results demonstrated the effectiveness of the proposed controller.

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Fractional-order switching type control law design for adaptive sliding mode technique of 3D fractional-order nonlinear systems

Complexity ◽

10.1002/cplx.21696 ◽

2015 ◽

Vol 21 (6) ◽

pp. 363-373 ◽

Cited By ~ 32

Author(s):

Chun Yin ◽

Yuhua Cheng ◽

Shou-Ming Zhong ◽

Zhanbing Bai

Keyword(s):

Nonlinear Systems ◽

Fractional Order ◽

Sliding Mode ◽

Control Law ◽

Adaptive Sliding Mode ◽

Switching Type ◽

Mode Technique ◽

Sliding Mode Technique

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

Advances in Difference Equations ◽

10.1186/s13662-019-2423-7 ◽

2019 ◽

Vol 2019 (1) ◽

Cited By ~ 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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Synchronization of Non-Integer Complex Chaotic Systems with Uncertainty and Disturbances via Adaptive Sliding Mode Technique

Journal of Scientific Research ◽

10.3329/jsr.v12i2.43780 ◽

2020 ◽

Vol 12 (2) ◽

pp. 189-200 ◽

Cited By ~ 1

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.

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