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On the Controllability of Anomalous Diffusions Generated by the Fractional Laplacian.
- Source :
-
Mathematics of Control, Signals & Systems . Sep2006, Vol. 18 Issue 3, p260-271. 12p. - Publication Year :
- 2006
-
Abstract
- This paper introduces a “spectral observability condition” for a negative self-adjoint operator which is the key to proving the null-controllability of the semigroup that it generates, and to estimating the controllability cost over short times. It applies to the interior controllability of diffusions generated by powers greater than 1/2 of the Dirichlet Laplacian on manifolds, generalizing the heat flow. The critical fractional order 1/2 is optimal for a similar boundary controllability problem in dimension one. This is deduced from a subsidiary result of this paper, which draws consequences on the lack of controllability of some one-dimensional output systems from Müntz–Szász theorem on the closed span of sets of power functions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09324194
- Volume :
- 18
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Mathematics of Control, Signals & Systems
- Publication Type :
- Academic Journal
- Accession number :
- 21679606
- Full Text :
- https://doi.org/10.1007/s00498-006-0003-3