A Black-Box method for parametric model order reduction based on matrix interpolation with application to simulation and control

Geuß, Matthias

doi:10.1515/auto-2016-0093

Cited by 3 publications

(3 citation statements)

References 103 publications

(187 reference statements)

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“…Algorithm 1 and the projection matrix W is chosen such that the matrix W T A 0 𝛼 V is nonsingular, then F i𝑗 = Fi𝑗 , where F ij and Fi𝑗 are defined as (11) and (20), respectively. It assumed that 𝛼 is chosen such that A 0 𝛼 is nonsingular.…”

Section: Theorem 1 If the Projection Matrix V Is Obtained Bymentioning

confidence: 99%

“…For the large‐scale parametric system, the goal is to obtain a reduced parametric system that can approximate the original parametric system for every parameter value in the parameter domain without repeating the reduction procedure. This technique is called parametric model order reduction (PMOR) [11,12].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, system for every parameter value in the parameter domain without repeating the reduction procedure. This technique is called parametric model order reduction (PMOR) [11,12].…”

Section: Introductionmentioning

confidence: 99%

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Laguerre‐based parametric order reduction for parametric systems by multi‐order Arnoldi

Yuan

Jiang

2022

Asian Journal of Control

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In this paper, a parametric model order reduction approach based on scaled Laguerre expansion series is investigated in frequency domain for large‐scale parametric systems. The proposed approach is implemented by two algorithms: the one‐sided algorithm and the two‐sided algorithm. Based on modified multi‐Arnoldi process for construction of projection matrices, reduced parametric systems with high fidelity are achieved in the full range of parametric domain. The reduced parametric systems obtained by the proposed algorithms preserve not only the parametric dependence of the original parametric system but also the first several Laguerre coefficients. The proposed algorithms are verified by two benchmarks (a synthetic parametric system and a microthruster unit). Comparisons of the results of original and reduced systems show that the obtained reduced systems have high fidelity.

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Section: Theorem 1 If the Projection Matrix V Is Obtained Bymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Laguerre‐based parametric order reduction for parametric systems by multi‐order Arnoldi

Yuan

Jiang

2022

Asian Journal of Control

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STABLE – a stability algorithm for parametric model reduction by matrix interpolation

Geuß

Lohmann

2016

Mathematical and Computer Modelling of Dynamical Systems

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In this article, an algorithm guaranteeing asymptotic stability for parametric model order reduction by matrix interpolation is proposed for the general class of high-dimensional linear time-invariant systems. In the first step, the system matrices of the high-dimensional parameter-dependent system are computed for a set of parameter vectors. The local highorder systems are reduced by a projection-based reduction method and stabilized, if necessary. Secondly, the low-order systems are transformed into a consistent set of generalized coordinates. Thirdly, a new procedure using semidefinite programming is applied to the low-order systems, converting them into strictly dissipative form. Finally, an asymptotically stable reduced order model can be calculated for any new parameter vector of interest by interpolating the system matrices of the local loworder models. We show that this approach works without any limiting conditions concerning the structure of the large-scale model and is suitable for real-time applications. The method is illustrated by two numerical examples. ARTICLE HISTORY

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On parametric structure preserving model order reduction of linear port-Hamiltonian systems

Scheuermann

Kotyczka

Lohmann

2019

At - Automatisierungstechnik

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A Black-Box method for parametric model order reduction based on matrix interpolation with application to simulation and control

Cited by 3 publications

References 103 publications

Laguerre‐based parametric order reduction for parametric systems by multi‐order Arnoldi

Laguerre‐based parametric order reduction for parametric systems by multi‐order Arnoldi

STABLE – a stability algorithm for parametric model reduction by matrix interpolation

On parametric structure preserving model order reduction of linear port-Hamiltonian systems

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