Interpolatory $\mathcal{H}_2$-optimality Conditions for Structured Linear Time-invariant Systems

Fuente: arXiv
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Main Authors: Mlinarić, Petar, Benner, Peter, Gugercin, Serkan
Format: Preprint
Published: 2023
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author Mlinarić, Petar
Benner, Peter
Gugercin, Serkan
author_facet Mlinarić, Petar
Benner, Peter
Gugercin, Serkan
contents Interpolatory necessary optimality conditions for $\mathcal{H}_2$-optimal reduced-order modeling of unstructured linear time-invariant (LTI) systems are well-known. Based on previous work on $\mathcal{L}_2$-optimal reduced-order modeling of stationary parametric problems, in this paper we develop and investigate optimality conditions for $\mathcal{H}_2$-optimal reduced-order modeling of structured LTI systems, in particular, for second-order, port-Hamiltonian, and time-delay systems. Under certain diagonalizability assumptions, we show that across all these different structured settings, bitangential Hermite interpolation is the common form for optimality, thus proving a unifying optimality framework for structured reduced-order modeling.
format Preprint
id arxiv_https___arxiv_org_abs_2310_10618
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Interpolatory $\mathcal{H}_2$-optimality Conditions for Structured Linear Time-invariant Systems
Mlinarić, Petar
Benner, Peter
Gugercin, Serkan
Numerical Analysis
Systems and Control
Optimization and Control
Interpolatory necessary optimality conditions for $\mathcal{H}_2$-optimal reduced-order modeling of unstructured linear time-invariant (LTI) systems are well-known. Based on previous work on $\mathcal{L}_2$-optimal reduced-order modeling of stationary parametric problems, in this paper we develop and investigate optimality conditions for $\mathcal{H}_2$-optimal reduced-order modeling of structured LTI systems, in particular, for second-order, port-Hamiltonian, and time-delay systems. Under certain diagonalizability assumptions, we show that across all these different structured settings, bitangential Hermite interpolation is the common form for optimality, thus proving a unifying optimality framework for structured reduced-order modeling.
title Interpolatory $\mathcal{H}_2$-optimality Conditions for Structured Linear Time-invariant Systems
topic Numerical Analysis
Systems and Control
Optimization and Control
url https://arxiv.org/abs/2310.10618