# On exact controllability of infinite-dimensional linear port-Hamiltonian systems

## TL;DR

This paper proves that well-posed infinite-dimensional linear port-Hamiltonian systems, including models like beams and waves, are exactly controllable with boundary control, expanding understanding of control in complex physical systems.

## Contribution

It establishes the exact controllability of a broad class of infinite-dimensional port-Hamiltonian systems with boundary control and no internal damping.

## Key findings

- Well-posed port-Hamiltonian systems are exactly controllable.
- Includes models of beams, waves, and transmission lines.
- Results apply to systems with state space L^2 and input space C^n.

## Abstract

Infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain with full boundary control and without internal damping are studied. This class of systems includes models of beams and waves as well as the transport equation and networks of nonhomogeneous transmission lines. The main result shows that well-posed port-Hamiltonian systems, with state space $L^2((0,1);\mathbb C^n)$ and input space $\mathbb C^n$, are exactly controllable.