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This paper investigates a model reduction problem for linear directed network systems, in which the interconnections among the vertices are described by general weakly connected digraphs. First, the definitions of pseudo controllability and…

Optimization and Control · Mathematics 2019-11-12 Xiaodong Cheng , Jacquelien M. A. Scherpen

The paper proposes a model reduction algorithm for linear hybrid systems, i.e., hybrid systems with externally induced discrete events, with linear continuous subsystems, and linear reset maps. The model reduction algorithm is based on…

Dynamical Systems · Mathematics 2020-03-19 Ion Victor Gosea , Mihaly Petreczky , John Leth , Rafael Wisniewski , Athanasios C. Antoulas

Dynamical systems with quadratic outputs have recently attracted significant attention. In this paper, we consider bilinear dynamical systems, a special class of weakly nonlinear systems, with a quadratic output. We develop various…

Numerical Analysis · Mathematics 2025-07-08 Heike Faßbender , Serkan Gugercin , Till Peters

Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…

Numerical Analysis · Mathematics 2024-06-11 Lei-Hong Zhang , Ren-Cang Li

In this paper, we study dimension reduction techniques for large-scale controlled stochastic differential equations (SDEs). The drift of the considered SDEs contains a polynomial term satisfying a one-sided growth condition. Such…

Probability · Mathematics 2023-03-10 Martin Redmann

We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP)…

Systems and Control · Computer Science 2012-08-13 Marc Peter Deisenroth , Ryan Turner , Marco F. Huber , Uwe D. Hanebeck , Carl Edward Rasmussen

In this paper, we consider the problem of quantifying controllability and observability of a nonlinear discrete time dynamical system. We introduce the Koopman operator as a canonical representation of the system and apply a lifting…

Systems and Control · Computer Science 2017-09-27 Enoch Yeung , Zhiyuan Liu , Nathan O. Hodas

Hybrid multiscale modelling has emerged as a useful framework for modelling complex biological phenomena. However, when accounting for stochasticity in the internal dynamics of agents, these models frequently become computationally…

Quantitative Methods · Quantitative Biology 2021-05-11 Daria Stepanova , Helen M. Byrne , Philip K. Maini , Tomás Alarcón

A common approach in model reduction is balanced truncation, which is based on gramian matrices classifiying certain attributes of states or parameters of a given dynamic system. Initially restricted to linear systems, the empirical…

Optimization and Control · Mathematics 2016-08-22 Christian Himpe , Mario Ohlberger

We tackle the problem of system identification, where we select inputs, observe the corresponding outputs from the true system, and optimize the parameters of our model to best fit the data. We propose a practical and computationally…

Systems and Control · Electrical Eng. & Systems 2025-10-02 Alexandros E. Tzikas , Mykel J. Kochenderfer

In this paper, the problem of full state approximation by model reduction is studied for stochastic and bilinear systems. Our proposed approach relies on identifying the dominant subspaces based on the reachability Gramian of a system. Once…

Numerical Analysis · Mathematics 2021-02-16 Martin Redmann , Igor Pontes Duff

Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…

Systems and Control · Electrical Eng. & Systems 2022-01-03 Mohamad Kazem Shirani Faradonbeh , Mohamad Sadegh Shirani Faradonbeh

While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…

Machine Learning · Statistics 2016-09-08 P. S. Koutsourelakis , Elias Bilionis

In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…

Numerical Analysis · Mathematics 2019-09-23 Roland Pulch , Akil Narayan

This paper studies the data-driven balanced truncation (BT) method for second-order systems based on the measurements in the frequency domain. The basic idea is to approximate Gramians used the numerical quadrature rules, and establish the…

Numerical Analysis · Mathematics 2025-06-05 Xiaolong Wang , Xuerong Yang , Xiaoli Wang , Bo Song

Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized (stochastic) partial differential equations and hence reduce computational complexity. A particular class of MOR techniques is balancing…

Optimization and Control · Mathematics 2019-03-29 Martin Redmann

This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse…

Dynamical Systems · Mathematics 2022-09-19 Harsh Sharma , Nicholas Galioto , Alex A. Gorodetsky , Boris Kramer

In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition…

Fluid Dynamics · Physics 2015-08-27 Thibault L. B. Flinois , Aimee S. Morgans , Peter J. Schmid

We consider two approaches to balanced truncation of stochastic linear systems, which follow from different generalizations of the reachability Gramian of deterministic systems. Both preserve mean-square asymptotic stability, but only the…

Dynamical Systems · Mathematics 2017-03-14 Peter Benner , Tobias Damm , Yolanda Rocio Rodriguez Cruz

This paper addresses the problem of model reduction for dynamical system models that describe biochemical reaction networks. Inherent in such models are properties such as stability, positivity and network structure. Ideally these…

Optimization and Control · Mathematics 2014-03-17 Aivar Sootla , James Anderson