arXiv subjects

Riccardo Morandin

Publications and source records attributed to Riccardo Morandin.

7 recordsLinked to original sources

arXiv2025

Discrete gradient methods for port-Hamiltonian differential-algebraic equations

Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient methods to the system class of nonlinear port-Hamiltonian differential-algebraic equations - as they emerge from the port- and energy-based modeling of physical systems in various domains. We introduce a novel numerical scheme tailored for semi-explicit differential-algebraic equations and further address more general settings using the concepts of discrete gradient pairs and Dirac-dissipative structures. Additionally, the behavior under system transformations is investigated and we demonstrate that under suitable assumptions port-Hamiltonian differential-algebraic equations admit a representation which consists of a parametrized port-Hamiltonian semi-explicit system and an unstructured equation. Finally, we present the application to multibody system dynamics and discuss numerical results to demonstrate the capabilities of our approach.

math.NA↗

arXiv2024

Dissipative energy functionals of passive linear time-varying systems

The concept of dissipativity plays a crucial role in the analysis of control systems. Dissipative energy functionals, also known as Hamiltonians, storage functions, or Lyapunov functions, depending on the setting, are extremely valuable to analyze and control the behavior of dynamical systems, but in general circumstances they are very difficult to compute, and not fully understood. In this paper we consider passive linear time-varying (LTV) systems, under very mild regularity assumptions, and their associated storage functions, as a necessary step to analyze general nonlinear systems. We demonstrate that every passive LTV system must have at least one time-varying positive semidefinite quadratic storage function, greatly reducing our search scope. Now focusing on quadratic storage functions, we analyze in detail their necessary regularity, which is lesser than continuous. Moreover, we prove that the rank of quadratic storage functions is nonincreasing in time, allowing us to introduce a novel null space decomposition, under much weaker assumptions than the one needed for general matrix functions. Additionally, we show a necessary kernel condition for the quadratic storage function, allowing us to reduce our search scope even further.

math.OC↗

arXiv2024

Relationship between dissipativity concepts for linear time-varying port-Hamiltonian systems

The relationship between different dissipativity concepts for linear time-varying systems is studied, in particular between port-Hamiltonian systems, passive systems, and systems with nonnegative supply. It is shown that linear time-varying port-Hamiltonian systems are passive, have nonnegative supply rates, and solve (under different smoothness assumptions) Kalman-Yakubovich-Popov differential and integral inequalities. The converse relations are also studied in detail. In particular, sufficient conditions are presented to obtain a port-Hamiltonian representation starting from any of the other dissipativity concepts. Two applications are presented.

math.OC↗

arXiv2023

Port-Hamiltonian Dynamic Mode Decomposition

We present a novel physics-informed system identification method to construct a passive linear time-invariant system. In more detail, for a given quadratic energy functional, measurements of the input, state, and output of a system in the time domain, we find a realization that approximates the data well while guaranteeing that the energy functional satisfies a dissipation inequality. To this end, we use the framework of port-Hamiltonian (pH) systems and modify the dynamic mode decomposition, respectively operator inference, to be feasible for continuous-time pH systems. We propose an iterative numerical method to solve the corresponding least-squares minimization problem. We construct an effective initialization of the algorithm by studying the least-squares problem in a weighted norm, for which we present the analytical minimum-norm solution. The efficiency of the proposed method is demonstrated with several numerical examples.

math.DS↗

arXiv2021

Error bounds for port-Hamiltonian model and controller reduction based on system balancing

We study linear quadratic Gaussian (LQG) control design for linear port-Hamiltonian systems. To this end, we exploit the freedom in choosing the weighting matrices and propose a specific choice which leads to an LQG controller which is port-Hamiltonian and, thus, in particular stable and passive. Furthermore, we construct a reduced-order controller via balancing and subsequent truncation. This approach is closely related to classical LQG balanced truncation and shares a similar a priori error bound with respect to the gap metric. By exploiting the non-uniqueness of the Hamiltonian, we are able to determine an optimal pH representation of the full-order system in the sense that the error bound is minimized. In addition, we discuss consequences for pH-preserving balanced truncation model reduction which results in two different classical H-infinity-error bounds. Finally, we illustrate the theoretical findings by means of two numerical examples.

math.OC↗

arXiv2019

Structure-preserving discretization for port-Hamiltonian descriptor systems

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 energy balance properties. In particular, port-Hamiltonian systems are naturally passive and Lyapunov stable, because the Hamiltonian defines a Lyapunov function. The explicit representation of input and dissipation in the structure make these systems particularly suitable for output feedback control. It is shown that this structure is invariant under a wide class of nonlinear transformations, and that it can be naturally modularized, making it adequate for automated modeling. We investigate then the application of time-discretization schemes to these systems and we show that, under certain assumptions on the Hamiltonian, structure preservation is achieved for some methods. Numerical examples are provided.

math.OC↗

arXiv2017

Qualitative Stability and Synchronicity Analysis of Power Network Models in Port-Hamiltonian Form

In view of highly decentralized and diversified power generation concepts, in particular with renewable energies such as wind and solar power, the analysis and control of the stability and the synchronization of power networks is an important topic that requires different levels of modeling detail for different tasks. A frequently used qualitative approach relies on simplified nonlinear network models like the Kuramoto model. Although based on basic physical principles, the usual formulation in form of a system of coupled ordinary differential equations is not always adequate. We present a new energy-based formulation of the Kuramoto model as port-Hamiltonian system of differential-algebraic equations. This leads to a very robust representation of the system with respect to disturbances, it encodes the underlying physics, such as the dissipation inequality or the deviation from synchronicity, directly in the structure of the equations, it explicitly displays all possible constraints and allows for robust simulation methods. Due to its systematic energy based formulation the model class allows easy extension, when further effects have to be considered, higher fidelity is needed for qualitative analysis, or the system needs to be coupled in a robust way to other networks. We demonstrate the advantages of the modified modeling approach with analytic results and numerical experiments.

cond-mat.dis-nn↗