Adaptive Sliding Control for a Class of Fractional Commensurate Order Chaotic Systems. (25th March 2015)

• Record Type: Journal Article
• Authors: Yuan, Jian; Shi, Bao; Yu, Zhentao
• Other Names: Sabatier Jocelyn Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2015(2015)
• Publication Date: 2015-03-25
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2015/972914
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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.