Exact observability and controllability for a nonsimple elastic rod. Issue 9 (4th July 2019)

• Record Type: Journal Article
• Authors: Aouadi, Moncef; Kassraoui, Jihed
• Is Part Of: Applicable analysis. Volume 98:Issue 9(2019)
• Page Start: 1705
• Page End: 1723
• Publication Date: 2019-07-04
• Subjects: Exact observability -- boundary controllability -- internal controllability -- Riesz basis -- Ingham theorem -- Hilbert Uniqueness Method (HUM); 93C20 -- 93B07; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1441993
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we prove exact observability, boundary and internal exact controllability results for a nonsimple elastic rod. By the spectral analysis method, it is shown that the considered problem has a sequence of eigenfunctions, which forms a Riesz basis for the state space. The exact observability is proved by application of a modified version of Ingham's Theorem. Then, via the Hilbert Uniqueness method, we prove a boundary controllability result with only one controller and an internal controllability result.