Related papers: Moving-Boundary Port-Hamiltonian Systems
In this paper, we extend the port-Hamiltonian framework by introducing the concept of Stokes-Lagrange structure, which enables the implicit definition of a Hamiltonian over an $N$-dimensional domain and incorporates energy ports into the…
Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian…
Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant…
We extend the port-Hamiltonian framework defined with respect to a Lagrangian submanifold and a Dirac structure by augmenting the Lagrangian submanifold with the space of external variables. The new pair of conjugated variables is called…
We consider an operator-theoretic approach to linear infinite-dimensional port-Hamiltonian systems. In particular, we use the theory of system nodes by Staffans to formulate a~suitable concept for port-Hamiltonian systems, which allows a…
This thesis deals with the formulation and analysis of two systems of conservation laws defined on two complementary intervals and coupled by some moving interface as a single infinite-dimensional port-Hamiltonian system. This approach may…
Electric circuits are usually described by charge- and flux-oriented modified nodal analysis. In this paper, we derive models as port-Hamiltonian systems on several levels: overall systems, multiply coupled systems and systems within…
A framework for identifying nonlinear port-Hamiltonian systems using input-state-output data is introduced. The framework utilizes neural networks' universal approximation capacity to effectively represent complex dynamics in a structured…
The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…
Methods for discretizing port-Hamiltonian systems are of interest both for simulation and control purposes. Despite the large literature on mixed finite elements, no rigorous analysis of the connections between mixed elements and…
Stability and stabilization of linear port-Hamiltonian systems on infinite-dimensional spaces are investigated. This class is general enough to include models of beams and waves as well as transport and Schr\"odinger equations with boundary…
This article presents an innovative approach to integrating port-Hamiltonian systems with neural network architectures, transitioning from deterministic to stochastic models. The study presents novel mathematical formulations and…
We present a gradient-based calibration algorithm to identify a port-Hamiltonian system from given time-domain input-output data. The gradient is computed with the help of sensitivities and the algorithm is tailored such that the structure…
An observer-based boundary controller for infinite-dimensional port-Hamiltonian systems defined on 1D spatial domains is proposed. The design is based on an early-lumping approach in which a finite-dimensional approximation of the…
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…
Dispersive time-decay estimates are proved for a one-parameter family of one-dimensional Dirac Hamiltonians with dislocations; these are operators which interpolate between two phase-shifted massive Dirac Hamiltonians at $x=+\infty$ and…
Stokes-Dirac structures are infinite-dimensional Dirac structures defined in terms of differential forms on a smooth manifold with boundary. These Dirac structures lay down a geometric framework for the formulation of Hamiltonian systems…
In this paper we introduce discrete gradient methods to discretize irreversible port-Hamiltonian systems showing that the main qualitative properties of the continuous system are preserved using this kind discretizations methods.
We study port-Hamiltonian systems on a familiy of intervals and characterise all boundary conditions leading to $m$-accretive realisations of the port-Hamiltonian operator and thus to generators of contractive semigroups. The proofs are…
We consider a port-Hamiltonian system on a spatial domain $\Omega \subseteq \mathbb{R}^n$ that is bounded with Lipschitz boundary. We show that there is a boundary triple associated to this system. Hence, we can characterize all boundary…