Boundary control systems on a one-dimension spatial domain

TL;DR

This paper establishes conditions for the well-posedness of boundary control systems on a 1D domain and links well-posedness to controllability and observability, demonstrated through Euler-Bernoulli beam models.

Contribution

It provides a necessary and sufficient condition for well-posedness and connects it to controllability and observability for boundary control systems.

Findings

Derived a necessary and sufficient condition for well-posedness.

Showed that well-posedness implies controllability and observability.

Applied results to Euler-Bernoulli beam models.

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.