Nonlinear Dynamics

, Volume 82, Issue 1–2, pp 39–52 | Cite as

Adaptive fractional-order switching-type control method design for 3D fractional-order nonlinear systems

  • Chun YinEmail author
  • Yuhua Cheng
  • YangQuan Chen
  • Brandon Stark
  • Shouming Zhong
Original Paper


In this paper, an adaptive sliding mode technique based on a fractional-order (FO) switching-type control law is designed to guarantee robust stability for uncertain 3D FO nonlinear systems. A novel FO switching-type control law is proposed to ensure the existence of the sliding motion in finite time. Appropriate adaptive laws are shown to tackle the uncertainty and external disturbance. The calculation formula of the reaching time is analyzed and computed. The reachability analysis is visualized to show how to obtain a shorter reaching time. A stability criterion of the FO sliding mode dynamics is derived based on indirect approach to Lyapunov stability. Advantages of the proposed control scheme are illustrated through numerical simulations.


Fractional-order switching-type control law Sliding mode control Reaching time  3D fractional-order nonlinear system  Adaptive sliding mode technique 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Chun Yin
    • 1
    Email author
  • Yuhua Cheng
    • 1
  • YangQuan Chen
    • 2
  • Brandon Stark
    • 2
  • Shouming Zhong
    • 3
  1. 1.School of Automation EngineeringUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China
  2. 2.Mechatronics, Embedded Systems and Automation (MESA) Lab, School of EngineeringUniversity of California, MercedMercedUSA
  3. 3.School of Mathematics ScienceUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China

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