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Paul Van Dooren (Université catholique de Louvain)26/05/2025, 13:30Talk
We construct optimally robust port-Hamiltonian realizations of a given rational transfer function that represents a passive system. We show that the realization with a maximal passivity radius is a normalized port-Hamiltonian one. Its computation is linked to a particular solution of a linear matrix inequality that defines passivity of the transfer function, and we provide an algorithm to...
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Karim Cherifi (Wuppertal university)26/05/2025, 14:00Talk
Port-Hamiltonian (pH) systems are a natural way to model many physical processes. Numerous specialized numerical techniques have been created to take advantage of and maintain the structure of pH systems, such as model order reduction (MOR) and space- and time-discretization. In this work, we focus on the structure-preserving MOR of linear time-varying (LTV) pH systems. LTV systems appear...
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Timo Reis (Technische Universität Ilmenau)26/05/2025, 14:30Talk
We consider cables that interact with the electromagnetic field through radiation in a bidirectional way. We show that the port-Hamiltonian framework is well-suited to model this interaction. The cable is described by the telegraph equations, while the electromagnetic field is (unsurprisingly) described by Maxwell’s equations. The coupling goes via boundary conditions for the electric and...
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Serkan Gugercin (Virginia Tech)26/05/2025, 15:30Talk
Port-Hamiltonian systems have emerged as a fundamental framework for modeling a wide range of physical phenomena due to their energy-based structure and inherent stability properties. To address the complexity of such models, various structure-preserving model reduction techniques have been developed for both linear and nonlinear port-Hamiltonian dynamics. In this work, we focus on bilinear...
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Valeria Simoncini (Universita di Bologna)26/05/2025, 16:00Talk
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. The topic has attracted great interest within the numerical community in the past decade, thanks to the applicability of linear matrix equations in a growing number of applications. In this talk we will discuss recent developments in...
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Daniel Kressner (EPFL)26/05/2025, 16:30Talk
The Discrete Empirical Interpolation Method (DEIM) is an important tool in model reduction, significantly reducing the cost of evaluating a high-dimensional function if the function value is known to be nearly contained in a low-dimensional subspace. On a matrix level, DEIM requires one to select a well-conditioned square submatrix $U(I,:)$ of an orthonormal basis $U \in \mathbb R^{n\times...
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Markus Lohmayer (FAU Erlangen-Nürnberg)26/05/2025, 17:10
This talk introduces a compositional, energy-based modeling language for classical mechanics, electromagnetism, and irreversible thermodynamics. The formal, domain-specific language has a graphical syntax, whose expressions are morphisms in a symmetric monoidal category. This enables the straightforward modular and hierarchical composition of complex systems from simpler subsystems. Primitive...
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Till Peters (TU Braunschweig)26/05/2025, 17:10
We study so called bilinear-quadratic output (BQO) systems of the form
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$\dot{x}(t)=Ax(t)+\sum_{k=1}^mN_kx(t)u_k(t)+Bu(t)$ with initial condition $x(0)=0$ and output $y(t)=Cx(t)+\begin{bmatrix} x(t)^TM_1x(t)& \dots & x(t)^TM_px(t) \end{bmatrix}^T,$ where $A\in\mathbb{R}^{n\times n}, B\in \mathbb{R}^{n\times m}, C\in\mathbb{R}^{p\times n},N_k\in \mathbb{R}^{n\times n}$ for $k=1,\dots,m$,... -
Hanna Blazhko (Jagiellonian University)26/05/2025, 17:10
We provide a method for detecting Kronecker blocks of size two in port-Hamiltonian pencils of the form λE − (J − R)Q, where Q*E and R are positive definite, and J is skew-Hermitian.
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The method is based on first-order perturbation theory and randomization. Furthermore, we study the impact of proximity to unstable systems on the numerical solutions (via the midpoint rule) of the corresponding... -
Dorothea Hinsen (TU Berlin)26/05/2025, 17:10
Efficient mobility and sustainable transportation are crucial for driving economic growth and preserving the environment in today’s globalized society. However, the transportation sector, responsible for a substantial portion of energy consumption and CO2 emissions, presents a significant challenge for achieving sustainable and ecological transformations, especially in countries like Germany....
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Alessandro Borghi (TU Berlin)26/05/2025, 17:10
From the approximation of complex-valued functions to the reduction of dynamical systems, Hardy spaces provide a powerful framework for the analysis and construction of optimal rational approximants. One of the most widely used methods in linear model order reduction is the iterative rational Krylov algorithm (IRKA), designed to construct rational interpolants that satisfy the first order...
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Jonas Nicodemus (Stuttgart Center for Simulation Science (SC SimTech), University of Stuttgart)26/05/2025, 17:10
We present a novel passivation method, called KLAP, for linear time-invariant systems based on the Kalman-Yakubovich-Popov (KYP) lemma in low-rank factorized form.
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The passivation problem in our framework corresponds to finding a perturbation to a given non-passive system that renders the system passive while minimizing the $\mathcal{H}_2$ distance between the original non-passive and the... -
Shubhaditya Burela (TU Berlin)26/05/2025, 17:10
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing and deriving reduced-order models that can replace the full PDE system in solving the optimal control problem.
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Specifically, we explore the use of the... -
Attila Karsai (TU Berlin)26/05/2025, 17:10
Dynamical systems can be used to model a broad class of physical processes, and conservation laws give rise to system properties like passivity or port-Hamiltonian structure. An important problem in practical applications is to steer dynamical systems to prescribed target states, and feedback controllers combining a regulator and an observer are a powerful tool to do so. However, controllers...
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Jakob Niehues (Potsdam Institute for Climate Impact Research)26/05/2025, 17:10
Renewable energy sources such as wind turbines and solar cells are connected to the power grid via grid-forming inverters (GFIs), which can contribute to grid stability and synchronization. Their rollout presents a significant modeling challenge, as GFIs are a relatively new and complex technology, of which there is a limited practical and theoretical understanding. In fact, physics-based...
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Carsten Hartmann (BTU Cottbus-Senftenberg, Institut für Mathematik)26/05/2025, 17:10
The realisation of constraints by strong confining forces is a classical theme in mechanics. Constraining a mechanical system typically leads to a differential algebraic equation of differential index 3. Recently, there has been a growing interest in studying constrained stochastic differential equations, due to their relevance in molecular dynamics, material science, computational statistics,...
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Arijit Sarkar (Brandenburg University of Technology Cottbus - Senftenberg)26/05/2025, 17:10
As the demand for energy grows, energy systems are becoming increasingly complex. Current systems heavily rely on fossil fuels, leading to negative environmental impacts. To mitigate this, future systems are expected to feature a significant proportion of renewable sources, though these are often uncertain and intermittent. One solution to better allocate renewable resources involves enabling...
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Andrii Dmytryshyn (Chalmers University of Technology)26/05/2025, 17:10
Computing the complete eigenstructure of matrix pencils is a challenging problem. Small perturbations can change both the eigenvalues with their multiplicities, as well as the minimal indices of a given pencil. Recently, however, perturbation theory was used to compute eigenvalues of singular matrix pencils. In this poster, we investigate how the behavior of a general matrix pencil under small...
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Paul Schwerdtner (NYU)26/05/2025, 17:10
Approximating field variables and data vectors from sparse samples is a key challenge for model order reduction of nonlinear dynamical systems. Without utilizing sparse samples -- a process often referred to as hyper-reduction -- the online costs of the reduced model continue to scale with the dimension of the full model. In this talk, we present a new methodology for empirical sparse...
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Zdeněk Strakoš (Charles University Prague)27/05/2025, 09:00Talk
This contribution will address relationship between spectra of preconditioned self-adjoint PDE operators associated with boundary value problems and their approximations using generalized matrix eigenvalue problems arising from discretization. We will recall several results from operator theory literature, compare them with results on the generalised eigenvalue problem in the numerical PDE...
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Michał Wojtylak (Jagiellonian University, Kraków, Poland)27/05/2025, 09:30Talk
We provide a systematic theory of singular pencils $\lambda E-A$, with (possibly unbounded) operator coefficients in a Hilbert space. Apparently, the situation is more complicated than in the finite dimensional case. Several equivalent statements connected to the Kronecker canonical form become essentially different when the dimension is infinite.
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We show the relation of these concepts to... -
Jörg Liesen (TU Berlin)27/05/2025, 10:00Talk
Any (real or complex) square matrix $M$ can be split into $M=H+S$, where $H$ is the Hermitian and $S$ is the skew-Hermitian part of $M$. Interestingly, this splitting occurs naturally and with a physical meaning in applications that involve energy-based modeling using DAE systems in dissipative Hamiltonian form (dHDAEs). The applicability of this modeling approach has been demonstrated in...
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Michael Overton (New York University)27/05/2025, 11:00Talk
Robust controllers that stabilize dynamical systems even under disturbances and noise are often formulated as solutions of nonsmooth, nonconvex optimization problems. While methods such as gradient sampling can handle the nonconvexity and nonsmoothness, the costs of evaluating the objective function may be substantial, making robust control challenging for dynamical systems with...
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Christopher Beattie (Virginia Tech)27/05/2025, 11:30Talk
This talk concerns the challenge of identifying states of dynamic systems that operate across multiple time scales, ranging from youth to old age, drawing on personal experiences of the speaker in collaboration with V. Mehrmann.
The central state identification challenge arises from the fact that data is only accessible at the finest time scales, and may be rapidly forgotten (e.g.,...
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Rafikul Alam (IIT Guwahati)27/05/2025, 12:00Talk
Consider the linear time-invariant time-delay system (TDS)
$$ \begin{align*} \frac{\mathrm{d}\mathbf{x}(t)}{\mathrm{d}t} &= A_0 \mathbf{x}(t) + \sum_{j=1}^{N_1} A_j \mathbf{x}(t - \tau_j) + \sum_{j=1}^{N_2} B_j \mathbf{u}(t- t_j), \\\\ \mathbf{y}(t) &= \sum_{j=1}^{N_3} C_j \mathbf{x}(t-s_j) + \sum_{j=1}^{N_4} D_j \mathbf{u}(t-h_j), \end{align*} $$ where $\mathbf{x}(t) \in...
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Arjan van der Schaft (University of Groningen)27/05/2025, 14:00Talk
A classical topic in analog design is the study of input-output systems with extra structure. Recently, this interest is renewed by motivations stemming from e.g. neuro-computing, dynamical networks, and scalable control. In this talk we will discuss various, often related, symmetry structures for standard linear systems, including gradient systems, relaxation systems and input-output...
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Emre Mengi (Koc University)27/05/2025, 14:30Talk
We consider a matrix polynomial dependent on several parameters. The minimization of its spectral abscissa, the real part of its rightmost eigenvalue, over the parameters is motivated by stability considerations on the associated higher-order linear control system, yet comes with computational challenges especially due to the non-Lipschitz nature of the spectral abscissa. We instead propose...
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Punit Sharma (Indian Institute of Technology Delhi, India)27/05/2025, 15:00Talk
We consider linear time-invariant continuous control systems that are bounded real, also known as scattering passive. Our main theoretical contribution is to show the equivalence between such systems and port-Hamiltonian (PH) systems whose factors satisfy certain linear matrix inequalities. Based on this result, we propose a formulation for the problem of finding the nearest bounded real...
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Hoang Linh Vu (Vietnam National University Hanoi)27/05/2025, 15:30Talk
In this presentation, we explore the challenge of computing the stability region for a class of singular nonlinear continuous- and discrete-time systems. Under specific conditions, we derive topological properties of the stability region. After providing key characterizations of its boundary, we introduce a practical, direct method for computing this region. The proposed method involves...
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Hongguo Xu (University of Kansas)27/05/2025, 16:30Talk
We show how invariant subspaces will change when a defective matrix is perturbed. We focus on the case when an invariant subspace corresponding to the same size Jordan blocks of a single eigenvalue is perturbed. The perturbations are characterized in terms of fractional orders. As an application, we study a class of Hamiltonian matrices that are related to Riccati inequalities. We show how the...
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Shreemayee Bora (Indian Institute of Technology Guwahati)27/05/2025, 17:00Talk
It is well known that eigenvalues of a Hermitian matrix pencil $L(\lambda) = \lambda A - B,$ occur in pairs $(\lambda, \bar{\lambda})$ with eigenvalues, if any, on the extended real line being the ones where the symmetry breaks down. We refer to such eigenvalues as critical eigenvalues and study the problem of finding optimal Hermitian perturbations of $L(\lambda)$ when it is of even size...
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Vasile Sima (National Institute for Research & Development in Informatics (retired))27/05/2025, 17:30Talk
Block diagonalization algorithms have many applications, including computation of reciprocal condition numbers for eigenvalues and invariant or deflating subspaces of matrices or matrix pencils, respectively, fast computation of matrix functions, or of the response of linear time invariant standard or descriptor systems. For matrix pencils, this algorithm is applied to a matrix pair in a...
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Riccardo Morandin (OvGU Magdeburg)28/05/2025, 09:30Talk
Port-Hamiltonian systems extend Hamiltonian systems to incorporate network structure and energy exchanges through ports, enabling the modeling of open and interconnected systems from various physical domains. The interconnection of network components often leads to differential-algebraic equations (DAEs), which also include algebraic constraints, for example Kirchhoff's laws. To ensure that...
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Paul Kotyczka (TUM)28/05/2025, 10:00Talk
Different avenues exist for the thermodynamically consistent modeling of open multi-physical systems with reversible-irreversible couplings. Thermodynamically consistent means that both the first (energy conservation) and the second (entropy production) law of thermodynamics are reflected in the model structure and the numerical schemes derived therefrom.
Founded on the port-Hamiltonian...
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Manuel Schaller (TU Chemnitz)28/05/2025, 10:30Talk
Abstract. Infinite-dimensional state-space systems with boundary control and observation pose significant analytical challenges due to the typically unbounded nature of input and output maps. A common approach to establishing a solution theory, such as via a variation of constants formula, relies on the admissibility of input and output operators—an assumption that is often difficult to verify...
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David Watkins (Washington State University)28/05/2025, 11:30Talk
At the beginning of the era of electronic computing there was a big effort to produce software to make the newly constructed hardware useful. In the area of scientific computing, one need that was recognized early on was for efficient and reliable methods to compute the eigenvalues of a matrix. This need was met around 1960 by the so-called QR algorithm, especially the implicitly-shifted...
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Anton Arnold (TU Wien)28/05/2025, 12:00Talk
The "index of hypocoercivity" is defined via a coercivity-type estimate for the self-adjoint/skew-adjoint parts of the generator, and it quantifies `how degenerate' a hypocoercive evolution equation is, both for ODEs and for evolutions equations in a Hilbert space. We show that this index characterizes the polynomial decay of the propagator norm for short time and illustrate these concepts for...
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Froilán Dopico (Universidad Carlos III de Madrid)28/05/2025, 12:30Talk
The complete eigenstructure, or structural data, of a rational matrix R(s) is comprised by its invariant rational functions, both finite and at infinity, which determine its finite and infinite pole and zero structures, and by the minimal indices of its left and right null spaces. These quantities arise in many applications in control theory and have been thoroughly studied in numerous...
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