Multiple adaptive fuzzy Nussbaum-type functions design for stochastic nonlinear systems with fixed-time performance

Yongliang Yang, Guilong Liu, Qing Li, Choon Ki Ahn

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Nussbaum design has been successfully exploited to deal with uncertain systems with a single unknown control coefficient. However, it is challenging for the traditional Nussbaum method to efficiently handle the feedback control design with multiple unknown time-varying control coefficients because the multiple Nussbaum-type gains might mutually cancel out, which makes the Lyapunov-based stability analysis infeasible. To tackle this issue, a novel type of Nussbaum function is designed for the tracking problem of a class of stochastic strict-feedback nonlinear systems. In the presented Nussbaum design, the multiple unknown control coefficients are separately compensated, where the effect of mutual cancellation no longer exists and the Lyapunov stability analysis can be directly applied. Moreover, the proposed Nussbaum design is combined with the fixed-time stability theory, which ensures the settling time is bounded and independent of the initial condition. Within the adaptive fuzzy backstepping framework, it is shown that all signals in the closed-loop system remain bounded through the theoretical discussions. The simulation experiment is conducted to verify the effectiveness of the presented design for the continuous-time stochastic nonlinear dynamical system.

Original languageEnglish
Article number108767
JournalFuzzy Sets and Systems
Publication statusPublished - 2024 Jan 30

Bibliographical note

Publisher Copyright:
© 2023 Elsevier B.V.


  • Adaptive fuzzy backstepping
  • Fixed-time stability
  • Multiple Nussbaum-type functions
  • Stochastic systems

ASJC Scopus subject areas

  • Logic
  • Artificial Intelligence


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