A distributed optimal control problem for a semilinear parabolic partial differential equation is
investigated. The stability of locally optimal solutions with respect to perturbations of the …

In this article, it is shown that there exist a finite number of indicator functions, which allow us
to track an arbitrary given trajectory of the Schlögl model, by means of an explicit saturated …

The stabilizability of a general class of abstract parabolic-like equations is investigated, with
a finite number of actuators. This class includes the case of actuators given as delta …

Approximation of high dimensional functions is in the focus of machine learning and data-
based scientific computing. In many applications, empirical risk minimisation techniques …

The estimation of the full state of a nonautonomous semilinear parabolic equation is
achieved by a Luenberger-type dynamical observer. The estimation is derived from an …

The stabilizability to trajectories of the Schl\" ogl model is investigated in the norm of the
natural state space for strong solutions, which is strictly contained in the standard pivot …

In these notes we present some first ideas on the composition of tensor trains for the use in
scientific computing. We discuss the relation to deep neural networks and the potential role …

Exponential stabilization to time-dependent trajectories for the incompressible Navier–
Stokes equations is achieved with explicit feedback controls. The fluid is contained in a …

A receding horizon control framework is coupled with a Luenberger observer to construct an
output-based control input stabilizing parabolic equations. The actuators and sensors are …

An exponential Luenberger dynamical observer is proposed to estimate the state of a
general class of nonautonomous semilinear parabolic equations. The result can be applied …