The non-smoothness problem in disturbance observer design: A set-invariance-based adaptive fuzzy control method

Maolong Lv, Simone Baldi, Zongcheng Liu

Research output: Contribution to journalArticleScientificpeer-review

20 Citations (Scopus)
71 Downloads (Pure)

Abstract

This work removes the critical assumptions of continuity, differentiability, and state-independent boundedness, which are typical of compounded disturbances in disturbance observer-based adaptive designs. Crucial in removing such assumptions are a novel observer-based design with state-dependent gain in place of a constant one, and a novel set-invariance design. The designs use different a priori knowledge of the disturbance, but they can both handle state-dependent (e.g., possibly unbounded) disturbances, as well as non-smooth (e.g., non-differentiable and jump discontinuous) disturbances. The tracking error is proven to be as small as desired by appropriately choosing design parameters. For the second design, which uses the least a priori knowledge of the disturbance, stability is proven by enhancing Lyapunov theory with an invariant-set mechanism, so as to construct an appropriate compact set resulting an invariant set for the closed-loop trajectories.

Original languageEnglish
Article number8606962
Pages (from-to)598-604
JournalIEEE Transactions on Fuzzy Systems
Volume27
Issue number3
DOIs
Publication statusPublished - 2019

Keywords

  • Disturbance observer
  • fuzzy adaptive control
  • invariant set
  • non-differentiable disturbance

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