Exact observability and controllability for a nonsimple elastic rod

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.

KEYWORDS:

• Exact observability
• boundary controllability
• internal controllability
• Riesz basis
• Ingham theorem
• Hilbert Uniqueness Method (HUM)

AMS SUBJECT CLASSIFICATIONS:

• 93C20
• 93B07

Acknowledgements

The authors would like to thank the referees for their critical review and valuable comments which thoroughly improved the paper.

Notes

No potential conflict of interest was reported by the authors.