Adaptive sliding-mode control for fractional-order uncertain linear systems with nonlinear disturbances

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• 作者：Liping Chen (1)
  Ranchao Wu (2)
  Yigang He (1)
  Yi Chai (3)
  
  1. School of Electrical Engineering and Automation ; Hefei University of Technology ; Hefei ; 230009 ; China
  2. School of Mathematics ; Anhui University ; Hefei ; 230039 ; China
  3. School of Automation ; Chongqing University ; Chongqing ; 400044 ; China
  
• 关键词：Fractional ; order systems ; Sliding ; mode control ; Linear matrix inequalities ; Sliding ; mode surface
• 刊名：Nonlinear Dynamics
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：80
• 期：1-2
• 页码：51-58
• 全文大小：405 KB
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• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

The problem of designing a sliding-mode controller for a class of fractional-order uncertain linear perturbed systems with Caputo derivative is addressed in this paper. Sufficient conditions for the existence of sliding surfaces guaranteeing the asymptotic stability of the reduced-order sliding-mode dynamics are obtained in terms of linear matrix inequalities, based on which and stability theory of fractional-order nonlinear systems; the corresponding reaching motion controller is proposed, and the reaching time is also obtained. Moreover, the upper bounds of the nonlinear uncertainties are not required to be known in advance, which can be tuned by the designed adaptive law. Meanwhile, some problems for the sliding-mode controller for fractional-order systems in existing literatures are pointed out. A numerical example is presented to demonstrate the validity and feasibility of the obtained results.