Related papers: Koopman Generator Decomposition for Port-Hamiltoni…
Linear dynamical systems are fully characterized by their eigenspectra, accessible directly from the generator of the dynamics. For nonlinear systems governed by partial differential equations, no equivalent theory exists. We introduce Lie…
We study the geometric structure of the drift dynamics of Irreversible port-Hamiltonian systems. This drift dynamics is defined with respect to a product of quasi-Poisson brackets, reflecting the interconnection structure and the…
A port-Hamiltonian (pH) system formulation is a geometrical notion used to formulate conservation laws for various physical systems. The distributed parameter port-Hamiltonian formulation models infinite dimensional Hamiltonian dynamical…
For a general class of nonlinear port-Hamiltonian systems we develop a high-order time discretization scheme with certain structure preservation properties. The finite or infinite-dimensional system under consideration possesses a…
We present a new balancing-based structure-preserving model reduction technique for linear port-Hamiltonian descriptor systems. The proposed method relies on a modification of a set of two dual generalized algebraic Riccati equations that…
We extend the modeling framework of port-Hamiltonian descriptor systems to include under- and over-determined systems and arbitrary differentiable Hamiltonian functions. This structure is associated with a Dirac structure that encloses its…
We study the optimal design of numerical integrators for dissipative systems, for which there exists an underlying thermodynamic structure known as GENERIC (general equation for the nonequilibrium reversible-irreversible coupling). We…
We reconsider the fundamental problem of coarse-graining infinite-dimensional Hamiltonian dynamics to obtain a macroscopic system which includes dissipative mechanisms. In particular, we study the thermodynamical implications concerning…
The anisotropic and heterogeneous $N$-dimensional wave equation, controlled and observed at the boundary, is considered as a port-Hamiltonian system. A recent structure-preserving mixed Galerkin method is applied, leading directly to a…
This paper presents an interpretable machine learning approach that characterizes load dynamics within an operator-theoretic framework for electricity load forecasting in power grids. We represent the dynamics of load data using the Koopman…
The Koopman operator has gained significant attention in recent years for its ability to verify evolutionary properties of continuous-time nonlinear systems by lifting state variables into an infinite-dimensional linear vector space. The…
This paper contributes with a new formal method of spatial discretization of a class of nonlinear distributed parameter systems that allow a port-Hamiltonian representation over a one dimensional manifold. A specific finite dimensional…
We study the structure of the generator of a symmetric, conservative quantum dynamical semigroup with norm-bounded generator on a von Neumann algebra equipped with a faithful semifinite trace. For von Neumann algebras with abelian commutant…
We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i)…
The Hamiltonian approach to isomonodromic deformation systems for generic rational covariant derivative operators on the Riemann sphere, having any matrix dimension $r$ and any number of isolated singularities of arbitrary Poincar\'e rank,…
We develop a unified geometric framework for mechanical systems that combine conservative and dissipative dynamics by formulating them on contact manifolds. Within this setting, we identify the Reeb vector field as the intrinsic generator…
The structure of continuous Hopfield networks is revisited from a system-theoretic point of view. After adopting a novel electrical network interpretation involving nonlinear capacitors, it is shown that Hopfield networks admit a…
We consider infinite dimensional port-Hamiltonian systems. Based on a power balance relation we introduce the port-Hamiltonian system representation where we pay attention to two different scenarios, namely the non-differential operator…
The representations of Galilean generators are constructed on a space where both position and momentum coordinates are noncommutating operators. A dynamical model invariant under noncommutative phase space transformations is constructed.…
In this paper, we develop high-order splitting methods for linear port-Hamiltonian systems, focusing on preserving their intrinsic structure, particularly the dissipation inequality. Port-Hamiltonian systems are characterized by their…