Novel command-filtered Nussbaum design for continuous-time nonlinear dynamical systems with multiple unknown high-frequency gains

Yongliang Yang, Liqiang Tang, Wencheng Zou, Choon Ki Ahn

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Command filters (CFs) have been successfully developed to reduce computational complexity and eliminate the effect of filtering errors on control performance through a compensating mechanism. However, to deal with multiple unknown high-frequency gains, the CF design remains an open problem due to the gap between the compensating mechanism design and unknown high-frequency gains. This paper bridges this gap by developing two additional adaptive laws that can contribute to the compensating mechanism design in novel CFs while considering the effect of unknown high-frequency gains. In the novel Nussbaum design, the influences of filtering errors are taken into account by introducing compensating signals. In contrast to existing filter-based Nussbaum methods, the compensating signals developed in this paper can handle multiple unknown high-frequency gains on the basis of the additional adaptive laws. The effect of filtering errors on the tracking performance is analyzed within the Lyapunov stability framework, and it is shown that the boundedness of all signals in the closed-loop system with the presented design can be guaranteed. Simulation results validate the efficacy of the proposed command-filtered Nussbaum design scheme.

Original languageEnglish
Pages (from-to)4313-4323
Number of pages11
JournalNonlinear Dynamics
Issue number5
Publication statusPublished - 2023 Mar

Bibliographical note

Funding Information:
This work was supported in part by the Natural Science Foundation of Beijing Municipality under Grant No. J210005, in part by the National Natural Science Foundation of China under Grant 61903028, and in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science and ICT) (No. NRF-2020R1A2C1005449).

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature B.V.


  • Multiple unknown high-frequency gains
  • Novel command filter design
  • Nussbaum-type function
  • Strict feedback nonlinear systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering


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