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Improved Stability for Linear SPDEs Using Mixed Boundary/Internal Controls

Abstract : This paper is motivated by the asymptotic stabilization of abstract SPDEs of linear type. As a first step, it proposes an abstract contribution to the exact controllability (in a general L p-sense, p > 1) of a class of linear SDEs with general time-invariant rank control coefficient in the diffusion term. From this point of view, our paper generalizes some of the results in [13] where full and null rank were considered. Necessary conditions and sufficient ones are discussed and their hierarchy and connections with the approximate controllability are illustrated. Second, our paper illustrates, on relevant frameworks of linear SPDEs, a way to drive exactly to 0 their unstable part of dimension n ≥ 1 by using M internal, respectively N boundary controls such that max {M, N } < n. Extensive examples are presented as is the minimal gain for judicious control pairs.
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https://hal.archives-ouvertes.fr/hal-03155340
Contributor : Dan Goreac Connect in order to contact the contributor
Submitted on : Monday, March 1, 2021 - 5:28:18 PM
Last modification on : Thursday, September 29, 2022 - 2:21:15 PM
Long-term archiving on: : Sunday, May 30, 2021 - 8:27:51 PM

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  • HAL Id : hal-03155340, version 1

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Dan Goreac, Ionut Munteanu. Improved Stability for Linear SPDEs Using Mixed Boundary/Internal Controls. Systems & Control Letters, 2021, 156. ⟨hal-03155340⟩

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