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Journal Articles SIAM Journal on Control and Optimization Year : 2021

Worst Exponential Decay Rate for Degenerate Gradient flows subject to persistent excitation

Abstract

In this paper we estimate the worst rate of exponential decay of degenerate gradient flows (x) over dot = -Sx, issued from adaptive control theory. Under persistent excitation assumptions on the positive semidefinite matrix S, we provide upper bounds for this rate of decay consistent with previously known lower bounds and analogous stability results for more general classes of persistently excited signals. The strategy of proof consists in relating the worst decay rate to optimal control questions and studying in detail their solutions. As a by-product of our analysis, we also obtain estimates for the worst L-2-gain of the time-varying linear control systems (x) over dot = -cc(inverted perpendicular) x + u, where the signal c is persistently excited, thus solving an open problem posed by Rantzer in 1999.
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Dates and versions

hal-02792435 , version 1 (25-04-2024)

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Paolo Mason, Yacine Chitour, Dario Prandi. Worst Exponential Decay Rate for Degenerate Gradient flows subject to persistent excitation. SIAM Journal on Control and Optimization, 2021, 59 (4), pp.3040-3067. ⟨10.1137/20M1343427⟩. ⟨hal-02792435⟩
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