Well-posedness of a class of infinite-dimensional port-Hamiltonian systems with boundary control and observation

TL;DR

This paper characterizes the well-posedness of a broad class of infinite-dimensional port-Hamiltonian systems with boundary control, including Euler-Bernoulli beams, providing verifiable conditions and applying them to specific models.

Contribution

It introduces an easily checkable condition for the well-posedness of boundary-controlled port-Hamiltonian systems, extending understanding beyond Timoshenko beam models.

Findings

Internal well-posedness does not imply overall well-posedness for Euler-Bernoulli beams.

An equivalent condition for well-posedness is established.

Results are applied to various Euler-Bernoulli beam models.

Abstract

We characterize the well-posedness of a class of infinite-dimensional port-Hamiltonian systems with boundary control and observation. This class includes in particular the Euler-Bernoulli beam equations and more generally 1D linear infinite-dimensional port-Hamiltonian systems with boundary control and observation as well as coupled systems. It is known, that for the Timoshenko beam models internal well-posedness implies well-posedness of the overall system. By means of an example we show that this is not true for the Euler-Bernoulli beam models. An easy verifiable equivalent condition for well-posedness of the overall system will be presented. We will conclude the paper by applying the obtained results to several Euler-Bernoulli beam models.