Well-posedness and controllability of hyperbolic boundary control systems on a one-dimensional spatial domain

Abstract

The aim of this paper is to investigate the well-posedness of a class of boundary control and observation systems on a one dimensional spatial domain. We derive a necessary and sufficient condition characterizing the well-posedness of these systems. Furthermore, we show that the well-posedness and full control and observation implies exact controllability and exact observability. The theoretical results are illustrated using Euler-Bernoulli beam models.

arXiv commentThis work was supported and funded by the European Union (Horizon Europe MSCA project ModConFlex, grant number 101073558) and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) Project-ID 531152215 -- CRC 1701. 25 pages