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Observability for non-autonomous systems
Publikationstyp
Journal Article
Date Issued
2023
Sprache
English
Author(s)
Institut
Volume
61
Issue
1
Start Page
313
End Page
339
Citation
SIAM Journal on Control and Optimization 61 (1): 315-341 (2023)
Publisher DOI
Scopus ID
ArXiv ID
Publisher
SIAM
Peer Reviewed
true
We study non-autonomous observation systems align* ẋ(t) = A(t) x(t), y(t) = C(t) x(t), x(0) = x₀∈ X, align* where (A(t)) is a strongly measurable family of closed operators on a Banach space X and (C(t)) is a family of bounded observation operators from X to a Banach space Y. Based on an abstract uncertainty principle and a dissipation estimate, we prove that the observation system satisfies a final-state observability estimate in Lʳ(E; Y) for measurable subsets E ⊆ [0,T], T > 0. An application of the above result to families of uniformly strongly elliptic differential operators A(t) on Lᵖ(ℝᵈ) and observation operators C(t)u = 𝟏Ω₍t₎ u is presented. In this setting, we give sufficient and necessary geometric conditions on the family of sets (Ω(t)) such that the corresponding observation system satisfies a final-state observability estimate.
Subjects
Functional Analysis
Analysis of PDEs
Optimization and Control
35Q93, 47N70 (Primary) 93B07, 93B28 (Secondary)
DDC Class
510: Mathematik