TY - GEN
T1 - A Time-delay Approach for Sampled-data and Delayed Scalar Extremum Seeking
AU - Zhu, Yang
AU - Fridman, Emilia
AU - Oliveira, Tiago Roux
N1 - Publisher Copyright:
© 2021 IEEE.
PY - 2021
Y1 - 2021
N2 - This paper proposes a constructive approach for sampled-data delayed extremum seeking (ES) by using two time-delay approaches: one to averaging and another one to sampled-data control. We first investigate the continuous-time ES with square wave dithers and then expand the proposed time-delay method to its sampled-data implementation with constant delay. By transforming the ES system to a time-delay system, we have developed an improved stability analysis via a novel Lyapunov-Krasovskii functional (LKF). We derive the practical stability conditions in terms of linear matrix inequalities (LMIs) for the resulting time-delay system. Under the assumption of some known bounds on the extremum value of the map and its Hessian, the time-delay approach offers a quantitative calculation on the upper bounds of the dither-sampling period and the constant delays that the ES system is able to tolerate, as well as the ultimate bound of the extremum seeking error. The proposed method also provides a bound on the initial deviation starting from which the solution is ultimately bounded.
AB - This paper proposes a constructive approach for sampled-data delayed extremum seeking (ES) by using two time-delay approaches: one to averaging and another one to sampled-data control. We first investigate the continuous-time ES with square wave dithers and then expand the proposed time-delay method to its sampled-data implementation with constant delay. By transforming the ES system to a time-delay system, we have developed an improved stability analysis via a novel Lyapunov-Krasovskii functional (LKF). We derive the practical stability conditions in terms of linear matrix inequalities (LMIs) for the resulting time-delay system. Under the assumption of some known bounds on the extremum value of the map and its Hessian, the time-delay approach offers a quantitative calculation on the upper bounds of the dither-sampling period and the constant delays that the ES system is able to tolerate, as well as the ultimate bound of the extremum seeking error. The proposed method also provides a bound on the initial deviation starting from which the solution is ultimately bounded.
UR - http://www.scopus.com/inward/record.url?scp=85126031051&partnerID=8YFLogxK
U2 - 10.1109/CDC45484.2021.9682882
DO - 10.1109/CDC45484.2021.9682882
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AN - SCOPUS:85126031051
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 6073
EP - 6080
BT - 60th IEEE Conference on Decision and Control, CDC 2021
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 60th IEEE Conference on Decision and Control, CDC 2021
Y2 - 13 December 2021 through 17 December 2021
ER -