Extremum seeking for nonlinear uncertain systems: A small-gain synthesis

Qiyue Wang, Zhengyan Qin, Tengfei Liu, Zhong Ping Jiang

Research output: Contribution to journalConference articlepeer-review


This paper studies the extremum seeking problem for static maps with the inputs of the maps generated by a nonlinear uncertain system. A new small-gain approach is developed which uses an extremum seeking strategy to generate a reference signal, and employs a control law for reference-tracking of the nonlinear uncertain systems. The notions of input-to-state stability (ISS) and input-to-output stability (IOS) are used to characterize the interconnection between the extremum seeking strategy and the reference-tracking controller, and the nonlinear small-gain theorem is employed to guarantee the stability of the closed-loop extremum seeking system. With the proposed approach, the extremum seeking problem for a complex nonlinear system is solvable as long as one can design a proper reference-tracking controller for the system. Examples are given to show the feasibility of the proposed approach, and a numerical simulation is employed to show the effectiveness of the proposed design.

Original languageEnglish (US)
Pages (from-to)5411-5416
Number of pages6
Issue number2
StatePublished - 2020
Event21st IFAC World Congress 2020 - Berlin, Germany
Duration: Jul 12 2020Jul 17 2020


  • Extremum seeking
  • Semi-global practical stabilization
  • Small-gain theorem

ASJC Scopus subject areas

  • Control and Systems Engineering


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