The Set-Invariance Paradigm in Fuzzy Adaptive DSC Design of Large-Scale Nonlinear Input-Constrained Systems

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Abstract

This paper proposes a novel set-invariance adaptive dynamic surface control (DSC) design for a larger class of uncertain large-scale nonlinear input-saturated systems. The peculiarity of this class is that no a priori bound on the continuous control gain functions is assumed (i.e., their boundedness cannot be assumed before obtaining system stability). This requires a new design. Differently from the available methods, the proposed design involves the construction of appropriate invariant sets for the closed-loop trajectories, which allows to remove the restrictive assumption of a priori bounds of the control gain functions. Furthermore, we show that such set-invariance design can handle input constraints in the form of input saturation. In line with the DSC methodology, semi-globally uniformly ultimate boundedness is proven: however, differently from the standard methodology, stability analysis requires the combination of Lyapunov and invariant set theories.

Original languageEnglish
Pages (from-to)1035-1045
JournalIEEE Transactions on Systems, Man, and Cybernetics: Systems
Volume51
Issue number2
DOIs
Publication statusPublished - 2021

Keywords

  • Adaptive fuzzy control
  • dynamic surface control (DSC)
  • input constraints
  • invariant set theory

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