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

作者：Yuan Jian^*; Shi Bao; Yu Zhentao

来源：Mathematical Problems in Engineering, 2015, 2015: 972914.

DOI：10.1155/2015/972914

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.

• 出版日期2015
• 单位中国人民解放军海军潜艇学院; 中国人民解放军海军航空工程学院