Improved stability for linear SPDEs using mixed boundary/internal controls

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 Lp-sense, p>1) of a class of linear SDEs with general time-invariant rank control coefficient in the diffusion...

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Bibliographic Details
Published in:Systems & control letters 2021-10, Vol.156, p.105024, Article 105024
Main Authors: Goreac, Dan, Munteanu, Ionut
Format: Article
Language:English
Subjects:
(Stochastic) Partial differential equations
Asymptotic stability
Exact controllability
Mathematics
Optimization and Control
Stochastic control
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Summary: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 Lp-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 Wang et al. (2017) 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 maxM,N
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2021.105024