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...
We study so called bilinear-quadratic output (BQO) systems of the form
$\dot{x}(t)=Ax(t)+\sum_{k=1}^mN_kx(t)u_k(t)+Bu(t)$ 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 $k=1,\dots,m$,...
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.
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...
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....
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...
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.
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...
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.
Specifically, we explore the use of the...
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...
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...
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,...
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...
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...
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...
