Searcharxiv⌕ Search

arXiv subjects

René Hosfeld

Publications and source records attributed to René Hosfeld.

5 recordsLinked to original sources
arXiv2026

Well-posedness and passivity for a class of bilinear control systems

We study an abstract class of bilinear infinite-dimensional systems that arises in various applications, including district heating systems and quantum control. First, we analyze the existence of mild and classical solutions for abstract bilinear systems with admissible input operators in Banach spaces and study continuous dependence on the data. When the underlying space is a Hilbert space, these results are used to show passivity for a suitably defined co-located output and for mild solutions. The results are applied to the bilinear Schrödinger equation, the Fokker--Planck equation, and a district heating or cooling pipe.

math.AP↗
arXiv2024

Input-to-state stability for bilinear feedback systems

Input-to-state stability estimates with respect to small initial conditions and input functions for infinite-dimensional systems with bilinear feedback are shown. We apply the obtained results to controlled versions of a viscous Burger equation with Dirichlet boundary conditions, a Schrödinger equation, a Navier--Stokes system and a semilinear wave equation.

math.AP↗
arXiv2023

BIBO stability for funnel control: semilinear internal dynamics with unbounded input and output operators

This note deals with Bounded-Input-Bounded-Output (BIBO) stability for semilinear infinite-dimensional dynamical systems allowing for boundary control and boundary observation. We give sufficient conditions that guarantee BIBO stability based on Lipschitz conditions with respect to interpolation spaces. Our results can be applied to guarantee feasibility of funnel control for coupled ODE-PDE systems, as shown by means of an example from chemical engineering.

math.OC↗
arXiv2022

Characterization of Orlicz admissibility

In this note we extend two characterizations of admissible operators with respect to $\mathrm{L}^p$ to more general Orlicz spaces. The equivalent conditions are given by the property that an associated operator generates a strongly continuous semigroup and in terms of a resolvent estimate.

math.FA↗