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On sampled-data extremum seeking control via stochastic approximation methods

Khong, Sei Zhen LU ; Tan, Ying; Nešić, Dragan and Manzie, Chris (2013) Asian Control Conference (ASCC2013)
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... (More)
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. (Less)
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publishing date
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Contribution to conference
publication status
published
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conference name
Asian Control Conference (ASCC2013)
external identifiers
  • Scopus:84886571607
language
English
LU publication?
no
id
56e94e5f-0841-45c2-88e8-5c3c63ee1091 (old id 4246754)
date added to LUP
2014-02-14 12:43:50
date last changed
2016-10-13 05:00:02
@misc{56e94e5f-0841-45c2-88e8-5c3c63ee1091,
  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.},
  author       = {Khong, Sei Zhen and Tan, Ying and Nešić, Dragan and Manzie, Chris},
  language     = {eng},
  title        = {On sampled-data extremum seeking control via stochastic approximation methods},
  year         = {2013},
}