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Conference Papers Year : 2020

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

Yacine Chitour
Paolo Mason
Dario Prandi

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.
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Dates and versions

hal-03020089 , version 1 (23-11-2020)

Identifiers

  • HAL Id : hal-03020089 , version 1

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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⟩
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