Birgit Jacob
A full characterization of the boundedness of Laplace--Carleson embeddings on $L^\infty$ is provided, in terms of the Carleson intensity of the respective measure and of a suitable weighted Berezin transform of the measure. Moreover,…
We derive a minimal port-Hamiltonian formulation of a general class of interacting particle systems driven by alignment and potential-based force dynamics which include the Cucker-Smale model with potential interaction and the second order…
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…
This paper deals with the problem of designing unknown input observers for a class of coupled semilinear wave partial differential equations (PDE) systems. A state observer is designed to estimate the uncertain coupled wave PDE systems.…
Infinite-dimensional differential algebraic equations (short DAEs) with input and output are studied. The concepts of operator nodes and system nodes are extended to systems which additionally may include algebraic constraints.…
We study integrated semigroups for infinite-dimensional differential-algebraic equations (DAEs) admitting a resolvent index. Building on the notion of integrated semigroups for the abstract Cauchy problem $\frac{d}{d t}x=Ax$, we extend this…
We propose a time domain decomposition approach to optimal control of partial differential equations (PDEs) based on semigroup theoretic methods. We formulate the optimality system consisting of two coupled forward-backward PDEs, the state…
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…
We study the Linear-Quadratic optimal control problem for a general class of infinite-dimensional passive systems, allowing for unbounded input and output operators. We show that under mild assumptions, the finite cost condition is always…
We derive an explicit solution to the operator Riccati equation solving the Linear-Quadratic (LQ) optimal control problem for a class of boundary controlled hyperbolic partial differential equations (PDEs). Different descriptions of the…
Linear-Quadratic optimal controls are computed for a class of boundary controlled, boundary observed hyperbolic infinite-dimensional systems, which may be viewed as networks of waves. The main results of this manuscript consist in…
A solution to the suboptimal $H^\infty$-control problem is given for a class of hyperbolic partial differential equations (PDEs). The first result of this manuscript shows that the considered class of PDEs admits an equivalent…
The solvability for infinite dimensional differential algebraic equations possessing a resolvent index and a Weierstra{\ss} form is studied. In particular, the concept of integrated semigroups is used to determine a subset on which…
We consider differential operators $A$ that can be represented by means of a so-called closure relation in terms of a simpler operator $A_{\operatorname{ext}}$ defined on a larger space. We analyze how the spectral properties of $A$ and…
A class of linear hyperbolic partial differential equations, sometimes called networks of waves, is considered. For this class of systems, necessary and sufficient conditions are formulated on the system matrices for the operator dynamics…
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…
Different index concepts for linear differential-algebraic equations are defined in the general Banach space setting, and compared. For regular finite-dimensional linear differential-algebraic equations, all these indices exist and are…
We present a gradient-based identification algorithm to identify the system matrices of a linear port-Hamiltonian system from given input-output time data. Aiming for a direct structure-preserving approach, we employ techniques from optimal…
A dynamic iteration scheme for linear differential-algebraic port-Hamil\-tonian systems based on Lions-Mercier-type operator splitting methods is developed. The dynamic iteration is monotone in the sense that the error is decreasing and no…
We provide an introduction to infinite-dimensional port-Hamiltonian systems. As this research field is quite rich, we restrict ourselves to the class of infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial…