A DSC method for strict-feedback nonlinear systems with possibly unbounded control gain functions

Maolong Lv, Ying Wang, Simone Baldi, Zongcheng Liu*, Zutong Wang

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

24 Citations (Scopus)
42 Downloads (Pure)


In dynamic surface control (DSC) methods, the control gain functions of systems are always assumed to be bounded, which is a restrictive assumption. This work proposes a novel DSC approach for an extended class of strict-feedback nonlinear systems whose control gain functions are continuous and possibly unbounded. Appropriate compact sets are constructed in such a way that the trajectories of the closed-loop system do not leave these sets, therefore, in these sets, maximums and minimums values of the continuous control gain functions are well defined even if the control gain functions are possibly unbounded. By using Lyapunov theory and invariant set theory, semi-globally uniformly ultimately boundedness is analytically proved: all the signals of closed-loop system will always stay in these compact sets, while the tracking error is shown to converge to a residual set that can be made as small as desired by adjusting design parameters appropriately. Finally, the effectiveness of the designed method is demonstrated via two examples.

Original languageEnglish
Pages (from-to)1383-1392
Publication statusPublished - 2018

Bibliographical note

Accepted Author Manuscript


  • Adaptive neural control
  • Dynamic surface control
  • Invariant set theory
  • Robust control


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