TY - GEN
T1 - A Time-delay Approach to Averaging for Bounded Extremum Seeking with Discontinuous Dither and Measurement Bias
AU - Shen, Hongyu
AU - Fridman, Emilia
AU - Su, Hongye
AU - Zhu, Yang
N1 - Publisher Copyright:
© 2022 American Automatic Control Council.
PY - 2022
Y1 - 2022
N2 - In this paper, we present a constructive method for the stability analysis of the bounded extremum seeking (ES) with discontinuous dithers and measurement bias, by using a time-delay approach to averaging. Discontinuous dithers used in ES are important for digital implementation. For conceptional clearness, we consider bounded ES of static maps in the case of single-input. By transforming the bounded ES dynamics into a time-delay system where the delay length is equal to the period of dither signal, we derive the efficient practical stability conditions for the resulting time-delay system in the form of linear matrix inequalities (LMIs). The stability of the transformed time-delay system guarantees the stability of the original ES plant. Under the assumption of the uncertain extremum point with the uncertain Hessian, the time-delay approach gives a quantitative calculation on the lower bound of the dither frequency and the upper bound on the resulting ultimate bound of seeking error. Fundamentally different from the classical averaging and Lie bracket methods for extremum seeking which are of approximate nature, the time-delay method proposed in the paper does not use any approximation via traditional averaging or Lie-bracket-based averaging.
AB - In this paper, we present a constructive method for the stability analysis of the bounded extremum seeking (ES) with discontinuous dithers and measurement bias, by using a time-delay approach to averaging. Discontinuous dithers used in ES are important for digital implementation. For conceptional clearness, we consider bounded ES of static maps in the case of single-input. By transforming the bounded ES dynamics into a time-delay system where the delay length is equal to the period of dither signal, we derive the efficient practical stability conditions for the resulting time-delay system in the form of linear matrix inequalities (LMIs). The stability of the transformed time-delay system guarantees the stability of the original ES plant. Under the assumption of the uncertain extremum point with the uncertain Hessian, the time-delay approach gives a quantitative calculation on the lower bound of the dither frequency and the upper bound on the resulting ultimate bound of seeking error. Fundamentally different from the classical averaging and Lie bracket methods for extremum seeking which are of approximate nature, the time-delay method proposed in the paper does not use any approximation via traditional averaging or Lie-bracket-based averaging.
UR - http://www.scopus.com/inward/record.url?scp=85138491334&partnerID=8YFLogxK
U2 - 10.23919/ACC53348.2022.9867299
DO - 10.23919/ACC53348.2022.9867299
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AN - SCOPUS:85138491334
T3 - Proceedings of the American Control Conference
SP - 5117
EP - 5122
BT - 2022 American Control Conference, ACC 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2022 American Control Conference, ACC 2022
Y2 - 8 June 2022 through 10 June 2022
ER -