Adaptive Finite-Time Stabilization of Chaotic Flow with a Single Unstable Node Using a Nonlinear Function-Based Global Sliding Mode

  • Saleh MobayenEmail author
  • Jun Ma
  • Gisela Pujol-Vazquez
  • Leonardo Acho
  • Quanmin Zhu
Research paper


This article presents a novel adaptive finite-time stabilization technique based on global sliding mode for disturbed chaotic flow with a single unstable node. The considered chaotic flow has unusual characteristics containing attractor merging, symmetry breaking, attracting tori and different forms of multi-stability. A nonlinear function is employed in the global sliding surface to modify damping ratio and improve the transient performance. The damping ratio of the closed-loop system is improved when the states converge to the origin. Using the new chattering-free controller, the reaching mode is removed and the sliding behavior is presented right from the first instant. The adaptive finite-time tuning law eliminates the requirement of the information about the disturbances’ bounds. Illustrative simulations are provided to display the efficiency of the proposed scheme.


Global sliding mode Adaptive gain tuning Finite-time control Chaotic flow Unstable node 



This work was partially supported by the Spanish Ministry of Economy, Industry and Competitiveness, under Grants DPI2016-77407-P (AEI/FEDER, UE) and DPI2015-64170-R (MINECO/FEDER).


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Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.Department of Electrical Engineering, Faculty of EngineeringUniversity of ZanjanZanjanIran
  2. 2.Department of PhysicsLanzhou University of TechnologyLanzhouChina
  3. 3.Department of MathematicsUniversitat Politècnica de Catalunya-BarcelonaTech (ESEIAAT)TerrasaSpain
  4. 4.Department of MathematicsUniversitat Politècnica de Catalunya-BarcelonaTech (EEBE)BarcelonaSpain
  5. 5.Department of Engineering Design and MathematicsUniversity of the West of EnglandBristolUK

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