Related papers: Koopman Generator Decomposition for Port-Hamiltoni…
We construct a discrete non-hermitean momentum operator, which implements faithfully the non self-adjoint nature of momentum for a particle in a box. Its eigenfunctions are strictly limited to the interior of the box in the continuum limit,…
We study how inexact nonlinear solvers lead to a loss of exact symplecticity in the Symplectic Euler (SE) and Stormer-Verlet (SV) schemes when applied to general nonseparable Hamiltonian systems. These schemes are implicit and require…
In this work we use the formalism of chord functions (\emph{i.e.} characteristic functions) to analytically solve quadratic non-autonomous Hamiltonians coupled to a reservoir composed by an infinity set of oscillators, with Gaussian initial…
It is well known that any port-Hamiltonian (pH) system is passive, and conversely, any minimal and stable passive system has a pH representation. Nevertheless, this equivalence is only concerned with the input-output mapping but not with…
In this paper we propose a novel approach to discretize linear port-Hamiltonian systems while preserving the underlying structure. We present a finite element exterior calculus formulation that is able to mimetically represent conservation…
In this contribution, a finite element scheme to impose mixed boundary conditions without introducing Lagrange multipliers is presented for hyperbolic systems described as port-Hamiltonian systems. The strategy relies on finite element…
The dynamic complexity of robots and mechatronic systems often pertains to the hybrid nature of dynamics, where governing equations consist of heterogenous equations that are switched depending on the state of the system. Legged robots and…
Koopman linear representations have become a popular tool for control design of nonlinear systems, yet it remains unclear when such representations are exact. In this paper, we establish sufficient and necessary conditions under which a…
In this paper we present a method for the addition of integral action to non-passive outputs of a class of port-Hamiltonian systems. The proposed integral controller is a dynamic extension, constructed from the open loop system, such that…
Hydrogen's growing role in the transition towards climate-neutral energy systems necessitates structured modeling frameworks. Existing gas network models, largely developed for natural gas, fail to capture hydrogen systems distinct…
The Koopman operator is a linear but infinite dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system, and is a powerful tool for the analysis and decomposition of…
We develop a framework for dimension reduction, mode decomposition, and nonparametric forecasting of data generated by ergodic dynamical systems. This framework is based on a representation of the Koopman and Perron-Frobenius groups of…
This work extends the high-resolution isogeometric analysis approach established for scalar transport equations to the equations of gas dynamics. The group finite element formulation is adopted to obtain an efficient assembly procedure for…
Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the…
We consider an anisotropic homogenized composite medium (HCM) arising from isotropic particulate component phases based on ellipsoidal geometries. For cubically nonlinear component phases, the corresponding zeroth-order…
This paper introduces a hypothetical hybrid control framework for port-Hamiltonian (p$\mathcal{H}$) systems, employing a dynamic decomposition based on Data-Assisted Control (DAC). The system's evolution is split into two parts with fixed…
Understanding the structure and stability of open quantum dynamics is increasingly important for both fundamental studies of nonequilibrium quantum systems and the development of quantum simulation algorithms. In this work, we introduce a…
This paper extends previous work on finitedifference schemes over staggered grids for infinite-dimensional port-Hamiltonian systems. In the one-dimensional setting, it generalizes the discretization approach originally developed for the…
We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…
In this contribution, we extend the hybridization framework for the Hodge Laplacian [Awanou et al., Hybridization and postprocessing in finite element exterior calculus, 2023] to port-Hamiltonian systems describing linear wave propagation…