A Tangential Interpolation Algorithm for Optimal H2 Model Reduction with Stability Guarantee

Zeng, Taishan; Chen, Jian; Lu, Chunyuan

doi:10.1109/iccis.2013.257

Cited by 2 publications

(5 citation statements)

References 12 publications

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“…While stability of the reduced-order model is not a priori guaranteed, it can be achieved with a "good" initialization step. In [30] a variation of the IRKA algorithm that guarantees stability is given.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Remark 9. The relation (30) holds in general and can be used also when u = Lω. In fact, it is easy to show that (30) gives the same result as ( 28) for u = Lω.…”

Section: The Input Of the System Is U = Lωmentioning

confidence: 99%

“…the determination of optimal H 2 (or other norms) reduced-order models, see e.g. [20,21,22,23,24,25,26,27,28,29,16,30]. The main difference between these works and the problem that we are studying is that the reduced-order model to be optimized is constrained to interpolate a given class of input signals or, equivalently, interpolate a given set of points.…”

Section: Introductionmentioning

confidence: 99%

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Data-driven constrained optimal model reduction

Scarciotti

Jiang

Astolfi

2020

European Journal of Control

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Model reduction by moment matching can be interpreted as the problem of finding a reduced-order model which possesses the same steady-state output response of a given full-order system for a prescribed class of input signals. Little information regarding the transient behavior of the system is systematically preserved, limiting the use of reduced-order models in control applications. In this paper we formulate and solve the problem of constrained optimal model reduction. Using a data-driven approach we determine an estimate of the moments and of the transient response of a possibly unknown system. Consequently we determine a reduced-order model which matches the estimated moments at the prescribed interpolation signals and, simultaneously, possesses the estimated transient. We show that the resulting system is a solution of the constrained optimal model reduction problem. Detailed results are obtained when the optimality criterion is formulated with the time-domain 1 , 2 , ∞ norms and with the frequency-domain H 2 norm. The paper is illustrated by two examples: the reduction of the model of the vibrations of a building and the reduction of the Eady model (an atmospheric storm track model).

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Section: Problem Formulationmentioning

confidence: 99%

“…Remark 9. The relation (30) holds in general and can be used also when u = Lω. In fact, it is easy to show that (30) gives the same result as ( 28) for u = Lω.…”

Section: The Input Of the System Is U = Lωmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Data-driven constrained optimal model reduction

Scarciotti

Jiang

Astolfi

2020

European Journal of Control

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“…Many researchers have studied the problem of optimal H 2 (or other norms) model reduction, see e.g. [17], [25]- [35]. However, to the best of the authors' knowledge, this is the first time that the reduced-order model to be optimized is constrained G. Scarciotti is with the Dept.…”

Section: Introductionmentioning

confidence: 99%

“…In [17] the IRKA algorithm is proposed: the output of the algorithm converges to an optimal (not necessarily stable) model. In [35] a variation of the IRKA algorithm that guarantees stability is given.…”

Section: B Problem Formulationmentioning

confidence: 99%

Constrained optimal reduced-order models from input/output data

Scarciotti

Jiang

Astolfi

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-Model reduction by moment matching does not preserve, in a systematic way, the transient response of the system to be reduced, thus limiting the use of this model reduction technique in control problems. With the final goal of designing reduced-order models which can effectively be used (not just for analysis but also) for control purposes, we determine, using a data-driven approach, an estimate of the moments and of the transient response of an unknown system. We compute the unique, up to a change of coordinates, reducedorder model which possesses the estimated transient and, simultaneously, achieves moment matching at the prescribed interpolation points. The error between the output of the system and the output of the reduced-order model is minimized and we show that the resulting system is a constrained optimal (in a sense to be specified) reduced-order model. The results of the paper are illustrated by means of a simple numerical example.

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A Tangential Interpolation Algorithm for Optimal H2 Model Reduction with Stability Guarantee

Cited by 2 publications

References 12 publications

Data-driven constrained optimal model reduction

Data-driven constrained optimal model reduction

Constrained optimal reduced-order models from input/output data

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