Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups

Karsten Kruse, Christian Seifert*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)
16 Downloads (Pure)

Abstract

We consider final state observability estimates for bi-continuous semigroups on Banach spaces, i.e. for every initial value, estimating the state at a final time T> 0 by taking into account the orbit of the initial value under the semigroup for t∈ [0 , T] , measured in a suitable norm. We state a sufficient criterion based on an uncertainty relation and a dissipation estimate and provide two examples of bi-continuous semigroups which share a final state observability estimate, namely the Gauß–Weierstraß semigroup and the Ornstein–Uhlenbeck semigroup on the space of bounded continuous functions. Moreover, we generalise the duality between cost-uniform approximate null-controllability and final state observability estimates to the setting of locally convex spaces for the case of bounded and continuous control functions, which seems to be new even for the case of Banach spaces.

Original languageEnglish
Pages (from-to)421-443
Number of pages23
JournalSemigroup forum
Volume106
Issue number2
DOIs
Publication statusPublished - Apr 2023
Externally publishedYes

Keywords

  • Bi-continuous semigroups
  • Cost-uniform approximate null-controllability
  • Final state observability estimate
  • Mixed topology
  • Saks space

Fingerprint

Dive into the research topics of 'Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups'. Together they form a unique fingerprint.

Cite this