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This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of…

Optimization and Control · Mathematics 2019-01-29 Xiaodong Cheng , Jacquelien M. A. Scherpen , Bart Besselink

Model order reduction involves constructing a reduced-order approximation of a high-order model while retaining its essential characteristics. This reduced-order model serves as a substitute for the original one in various applications such…

Systems and Control · Electrical Eng. & Systems 2024-03-06 Qiu-Yan Song , Umair Zulfiqar , Zhi-Hua Xiao , Mohammad Monir Uddin , Victor Sreeram

This work proposes a model-reduction methodology that preserves Lagrangian structure (equivalently Hamiltonian structure) and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence.…

Computational Engineering, Finance, and Science · Computer Science 2015-04-16 Kevin Carlberg , Ray Tuminaro , Paul Boggs

Reduced basis methods are popular for approximately solving large and complex systems of differential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model.…

Numerical Analysis · Mathematics 2018-03-20 Babak Maboudi Afkham , Jan S. Hesthaven

In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems. This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems. Specifically in this…

Optimization and Control · Mathematics 2013-03-19 Mihaly Petreczky , Rafael Wisniewski , John Leth

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…

Numerical Analysis · Mathematics 2021-04-23 B. C. van Huijgevoort , S. Weiland , H. J. Zwart

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…

Numerical Analysis · Mathematics 2023-01-06 Michael Günther , Birgit Jacob , Claudia Totzeck

We propose a linearly implicit structure-preserving numerical method for semilinear Hamiltonian systems with polynomial nonlinearities, combining Kahan's method and exponential integrator. This approach efficiently balances computational…

Numerical Analysis · Mathematics 2026-03-03 Pan Zhang , Fengyang Xiao , Lu Li

The proper orthogonal decomposition reduced-order models (POD-ROMs) have been widely used as a computationally efficient surrogate models in large-scale numerical simulations of complex systems. However, when it is applied to a Hamiltonian…

Numerical Analysis · Mathematics 2017-03-08 Yuezheng Gong , Qi Wang , Zhu Wang

We present a balanced truncation model reduction approach for a class of nonlinear systems with time-varying and uncertain inputs. First, our approach brings the nonlinear system into quadratic-bilinear~(QB) form via a process called…

Numerical Analysis · Mathematics 2020-10-29 Boris Kramer , Karen E. Willcox

We discuss balanced truncation model order reduction for large-scale quadratic-bilinear (QB) systems. Balanced truncation for linear systems mainly involves the computation of the Gramians of the system, namely reachability and…

Optimization and Control · Mathematics 2017-05-02 Peter Benner , Pawan Goyal

We present a new optimization-based structure-preserving model order reduction (MOR) method for port-Hamiltonian descriptor systems (pH-DAEs) with differentiation index two. Our method is based on a novel parameterization that allows us to…

Systems and Control · Electrical Eng. & Systems 2022-06-09 Tim Moser , Paul Schwerdtner , Volker Mehrmann , Matthias Voigt

This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To overcome the slowly decaying Kolmogorov width typical of…

Numerical Analysis · Mathematics 2022-02-02 Jan S. Hesthaven , Cecilia Pagliantini , Nicolò Ripamonti

We discuss structure-preserving time discretization for nonlinear port-Hamiltonian systems with state-dependent mass matrix. Such systems occur, for instance, in the context of structure-preserving nonlinear model order reduction for…

Numerical Analysis · Mathematics 2023-11-02 Philipp Schulze

We consider the linear quadratic Gaussian control problem with a discounted cost functional for descriptor systems on the infinite time horizon. Based on recent results from the deterministic framework, we characterize the feasibility of…

Optimization and Control · Mathematics 2020-04-21 Hermann Mena , Lena-Maria Pfurtscheller , Matthias Voigt

A standard approach for model reduction of linear input-output systems is balanced truncation, which is based on the controllability and observability properties of the underlying system. The related dominant subspace projection model…

Optimization and Control · Mathematics 2019-08-23 Peter Benner , Christian Himpe

Evolutionary partial differential equations play a crucial role in many areas of science and engineering. Spatial discretization of these equations leads to a system of ordinary differential equations which can then be solved by numerical…

Numerical Analysis · Mathematics 2024-11-22 F. K. J. Niggl

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)…

Dynamical Systems · Mathematics 2018-03-02 Paul Kotyczka , Bernhard Maschke , Laurent Lefèvre

In this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic…

Optimization and Control · Mathematics 2023-11-07 Tobias Damm , Martin Redmann

Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric \emph{nonlinear} Hamiltonian…

Numerical Analysis · Mathematics 2024-09-30 Cecilia Pagliantini , Federico Vismara