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

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 intro...

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Bibliographic Details
Main Authors: Jian Yuan, Bao Shi, Zhentao Yu
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2015/972914
Description
Summary: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.
ISSN:1024-123X
1563-5147