On sampled-data extremum seeking control via stochastic approximation methods

Sei Zhen Khong, Ying Tan, Dragan Nesic, Chris Manzie

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

This note establishes a link between stochastic approximation and extremum seeking of dynamical nonlinear systems. In particular, it is shown that by applying classes of stochastic approximation methods to dynamical systems via periodic sampled-data control, convergence analysis can be performed using standard tools in stochastic approximation. A tuning parameter within this framework is the period of the synchronised sampler and hold device, which is also the waiting time during which the system dynamics settle to within a controllable neighbourhood of the steady-state input-output behaviour. Semiglobal convergence with probability one is demonstrated for three basic classes of stochastic approximation methods: finite-difference, random directions, and simultaneous perturbation. The tradeoff between the speed of convergence and accuracy is also discussed within the context of asymptotic normality of the outputs of these optimisation algorithms.

Original languageEnglish (US)
Title of host publication2013 9th Asian Control Conference, ASCC 2013
DOIs
StatePublished - Oct 31 2013
Event2013 9th Asian Control Conference, ASCC 2013 - Istanbul, Turkey
Duration: Jun 23 2013Jun 26 2013

Publication series

Name2013 9th Asian Control Conference, ASCC 2013

Other

Other2013 9th Asian Control Conference, ASCC 2013
CountryTurkey
CityIstanbul
Period6/23/136/26/13

Keywords

  • Extremum seeking
  • recursive optimisation algorithms
  • sampled-data control
  • stochastic approximation

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