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标题：On the decay rate for degenerate gradient flows subject to persistent excitation ⁎
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作者：Yacine Chitour ; Paolo Mason ; Dario Prandi 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2020
卷号：53
期号：2
页码：1709-1714
DOI：10.1016/j.ifacol.2020.12.2246
语种：English
出版社：Elsevier
摘要：AbstractIn this paper, we study the worst rate of exponential decay for degenerate gradient flows in ℝnof the formẋ(t) = —c(t)c(t)Tx(t),issued from adaptative control theory, under a persistent excitation (PE) condition. That is, there exists a, b,T> 0 such that, for everyt≥ 0 it holds aIdn≤∫t+Ttc(s)c(s)Tds ≤bIdn. Our main result is an upper bound of the forma/(1+b)2Tto be compared with the well-known lower bounds of the form a/(1+nb2)T. As a byproduct, we also provide necessary conditions for the exponential convergence of these systems under a more general (PE) condition. Our techniques relate the worst rate of exponential decay to an optimal control problem that we study in detail.
关键词：KeywordsPersistent excitationDegenerate gradient flow