HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Conference papers

On the decay rate for degenerate gradient flows subject to persistent excitation

Abstract : In this paper, we study the worst rate of exponential decay for degenerate gradient flows in R n of the formẋ(t) = −c(t)c(t) x(t), issued from adaptative control theory, under a persistent excitation (PE) condition. That is, there exists a, b, T > 0 such that, for every t ≥ 0 it holds a Id n ≤ ∫ t+T t c(s)c(s) ds ≤ b Id n. Our main result is an upper bound of the form a (1+b) 2 T , to be compared with the well-known lower bounds of the form a (1+nb 2)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.
Document type :
Conference papers
Complete list of metadata

Contributor : Dario Prandi Connect in order to contact the contributor
Submitted on : Monday, November 23, 2020 - 4:44:12 PM
Last modification on : Tuesday, January 4, 2022 - 6:05:00 AM
Long-term archiving on: : Thursday, February 25, 2021 - 1:36:52 PM


Files produced by the author(s)


  • HAL Id : hal-03020089, version 1


Yacine Chitour, Paolo Mason, Dario Prandi. On the decay rate for degenerate gradient flows subject to persistent excitation. IFAC World Congress 2020, Germany, Jul 2020, Berlin (virtual), Germany. pp.1709-1714. ⟨hal-03020089⟩



Record views


Files downloads