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Extremum seeking of dynamical systems via gradient descent and stochastic approximation methods

Khong, Sei Zhen LU ; Tan, Ying; Manzie, Chris and Nesic, Dragan (2015) In Automatica 56. p.44-52
Abstract
This paper examines the use of gradient based methods for extremum seeking control of possibly infinite-dimensional dynamic nonlinear systems with general attractors within a periodic sampled-data framework. First, discrete-time gradient descent method is considered and semi-global practical asymptotic stability with respect to an ultimate bound is shown. Next, under the more complicated setting where the sampled measurements of the plant’s output are corrupted by an additive noise, three basic stochastic approximation methods are analysed; namely finite-difference, random directions, and simultaneous perturbation. Semi-global convergence to an optimum with probability one is established. A tuning parameter within the sampled-data... (More)
This paper examines the use of gradient based methods for extremum seeking control of possibly infinite-dimensional dynamic nonlinear systems with general attractors within a periodic sampled-data framework. First, discrete-time gradient descent method is considered and semi-global practical asymptotic stability with respect to an ultimate bound is shown. Next, under the more complicated setting where the sampled measurements of the plant’s output are corrupted by an additive noise, three basic stochastic approximation methods are analysed; namely finite-difference, random directions, and simultaneous perturbation. Semi-global convergence to an optimum with probability one is established. A tuning parameter within the sampled-data 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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Automatica
volume
56
pages
44 - 52
publisher
Pergamon
external identifiers
  • wos:000355047000006
  • scopus:84929407187
ISSN
0005-1098
DOI
10.1016/j.automatica.2015.03.018
language
English
LU publication?
yes
id
b3acce10-706d-4a18-a4b8-95e1d4fc1c5d (old id 5276016)
date added to LUP
2015-04-17 11:13:43
date last changed
2017-11-12 03:46:33
@article{b3acce10-706d-4a18-a4b8-95e1d4fc1c5d,
  abstract     = {This paper examines the use of gradient based methods for extremum seeking control of possibly infinite-dimensional dynamic nonlinear systems with general attractors within a periodic sampled-data framework. First, discrete-time gradient descent method is considered and semi-global practical asymptotic stability with respect to an ultimate bound is shown. Next, under the more complicated setting where the sampled measurements of the plant’s output are corrupted by an additive noise, three basic stochastic approximation methods are analysed; namely finite-difference, random directions, and simultaneous perturbation. Semi-global convergence to an optimum with probability one is established. A tuning parameter within the sampled-data 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.},
  author       = {Khong, Sei Zhen and Tan, Ying and Manzie, Chris and Nesic, Dragan},
  issn         = {0005-1098},
  language     = {eng},
  pages        = {44--52},
  publisher    = {Pergamon},
  series       = {Automatica},
  title        = {Extremum seeking of dynamical systems via gradient descent and stochastic approximation methods},
  url          = {http://dx.doi.org/10.1016/j.automatica.2015.03.018},
  volume       = {56},
  year         = {2015},
}