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Related papers: $\mathcal H_2$-Quasi-Optimal Model Order Reduction…

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This paper addresses the $\mathcal{H}_2$-optimal approximation of linear dynamical systems with quadratic-output functions, also known as linear quadratic-output systems. Our major contributions are threefold. First, we derive…

Numerical Analysis · Mathematics 2025-05-07 Sean Reiter , Ion Victor Gosea , Igor Pontes Duff , Serkan Gugercin

In this paper we study the problem of model reduction of linear network systems. We aim at computing a reduced order stable approximation of the network with the same topology and optimal w.r.t. H2 norm error approximation. Our approach is…

Optimization and Control · Mathematics 2019-05-21 I. Necoara , T. C. Ionescu

Linear time-invariant quadratic output (LTIQO) systems generalize linear time-invariant systems to nonlinear regimes. Problems of this class occur in multiple applications naturally, such as port-Hamiltonian systems, optimal control, and…

Optimization and Control · Mathematics 2025-05-20 Birgit Hillebrecht , Benjamin Unger

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

In this paper, we investigate the optimal $\mathcal{H}_2$ model reduction problem for single-input single-output (SISO) continuous-time linear time-invariant (LTI) systems. A semi-definite relaxation (SDR) approach is proposed to determine…

Optimization and Control · Mathematics 2025-08-26 Wenshan Zhu , Imad Jaimoukha

A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method, based on constructive algebra, guarantees that the global optimum is found; it does not involve any gradient-based…

Optimization and Control · Mathematics 2007-06-14 Bernard Hanzon , Jan M. Maciejowski , Chun Tung Chou

In order to solve partial differential equations numerically and accurately, a high order spatial discretization is usually needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized systems…

Optimization and Control · Mathematics 2017-12-04 Pawan Goyal , Martin Redmann

In this paper, the problems of frequency-limited and time-limited H2-optimal model order reduction of linear time-invariant systems are considered within the oblique projection framework. It is shown that it is inherently not possible to…

Systems and Control · Electrical Eng. & Systems 2021-09-15 Umair Zulfiqar , Victor Sreeram , Xin Du

In time-limited model order reduction, a reduced-order approximation of the original high-order model is obtained that accurately approximates the original model within the desired limited time interval. Accuracy outside that time interval…

Systems and Control · Electrical Eng. & Systems 2022-12-19 Umair Zulfiqar , Xin Du , Qiuyan Song , Zhi-Hua Xiao , Victor Sreeram

We develop the interpolatory $\mathcal{H}_2$ optimal model reduction framework for linear control systems posed on infinite dimensional state, input and output spaces. Specifically, we consider linear systems formulated as controlled…

Optimization and Control · Mathematics 2026-04-15 Cankat Tilki , Tobias Breiten , Serkan Gugercin

This paper presents an interpolatory framework for time-limited $H_2$ optimal model order reduction named Limited Time Iterative Rational Krylov Algorithm (LT-IRKA). The algorithm yields high fidelity reduced order models over limited time…

Systems and Control · Electrical Eng. & Systems 2021-10-12 Kasturi Das , Srinivasan Krishnaswamy , Somanath Majhi

A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique,…

Optimization and Control · Mathematics 2016-07-01 J. J. Trujillo , V. M. Ungureanu

We mainly consider the frequency limited $\mathcal{H}_2$ optimal model order reduction of large-scale sparse generalized systems. For this purpose we need to solve two Sylvester equations. This paper proposes efficient algorithm to solve…

Optimization and Control · Mathematics 2021-01-13 Xin Du , M. Monir Uddin , A. Mostakim Fony , Md. Tanzim Hossain , Mohammaed Sahadat-Hossain

In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…

Numerical Analysis · Mathematics 2024-08-29 Hendrik Kleikamp , Lukas Renelt

We formulate here an approach to model reduction that is well-suited for linear time-invariant control systems that are stabilizable and detectable but may otherwise be unstable. We introduce a modified $\mathcal{H}_2$-error metric, the…

Numerical Analysis · Mathematics 2019-10-01 Tobias Breiten , Chris A. Beattie , Serkan Gugercin

We introduce an interpolation framework for H-infinity model reduction founded on ideas originating in optimal-H2 interpolatory model reduction, realization theory, and complex Chebyshev approximation. By employing a Loewner "data-driven"…

Numerical Analysis · Mathematics 2013-09-03 Garret Flagg , Christopher Beattie , Serkan Gugercin

A simple nonlinear system modeling algorithm designed to work with limited \emph{a priori }knowledge and short data records, is examined. It creates an empirical Volterra series-based model of a system using an $l_{q}$-constrained least…

Systems and Control · Computer Science 2018-04-20 P. Śliwiński , A. Marconato , P. Wachel , G. Birpoutsoukis

For linear time-invariant (LTI) systems, the design of an optimal controller is a commonly encountered problem in many applications. Among all the optimization approaches available, the linear quadratic regulator (LQR) methodology certainly…

Optimization and Control · Mathematics 2022-03-29 Zilong Cheng , Jun Ma , Xiaocong Li , Masayoshi Tomizuka , Tong Heng Lee

We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system…

Optimization and Control · Mathematics 2011-06-15 Jake Bouvrie , Boumediene Hamzi

This paper provides an $H_2$ optimal scheme for reducing diffusively coupled second-order systems evolving over undirected networks. The aim is to find a reduced-order model that not only approximates the input-output mapping of the…

Optimization and Control · Mathematics 2021-11-18 Lanlin Yu , Xiaodong Cheng , Jacquelien M. A. Scherpen , Junlin Xiong