A note on the cross Gramian for non-symmetric systems

Himpe, Christian; Ohlberger, Mario

doi:10.1080/21642583.2016.1215273

Cited by 21 publications

(24 citation statements)

References 37 publications

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“…(25) holds [24], and Algorithm 2 yields the same H r (z) as Algorithm 1. [25], the definition in Eq. (24) can be extended to nonsymmetric systems as follows.…”

Section: Remark 6 Similar To the Standard Cross Gramian Definition Wmentioning

confidence: 78%

Model reduction of discrete-time systems in limited intervals

Zulfiqar¹,

Liaquat²

2018

Turk J Elec Eng & Comp Sci

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Abstract:Model order reduction (MOR) is a process of obtaining a lower order surrogate model that accurately approximates the original high-order system. Since no actuator or plant operates over the entire time and frequency ranges, the reduced-order model should be accurate in the actual range of operation. In this paper, model reduction techniques for discrete time systems are presented that ensure less reduction error in the specified time and frequency intervals. The techniques are tested on the benchmark numerical examples and their efficacy is shown.

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“…(25) holds [24], and Algorithm 2 yields the same H r (z) as Algorithm 1. [25], the definition in Eq. (24) can be extended to nonsymmetric systems as follows.…”

Section: Remark 6 Similar To the Standard Cross Gramian Definition Wmentioning

confidence: 78%

Model reduction of discrete-time systems in limited intervals

Zulfiqar¹,

Liaquat²

2018

Turk J Elec Eng & Comp Sci

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“…Future extensions will include expanding the scope of the empirical cross gramian beyond symmetric linear systems as in Himpe and Ohlberger (2014b), or gradient nonlinear systems to more general (non-symmetric) configurations Himpe and Ohlberger (2015).…”

Section: Remarks and Outlookmentioning

confidence: 99%

The Empirical Cross Gramian for Parametrized Nonlinear Systems

Himpe

Ohlberger

2015

IFAC-PapersOnLine

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The cross gramian matrix can be used for model order reduction as well as system identification of linear control systems, which are frequently used in the sciences. The empirical cross gramian is solely computed from trajectories and hence extends beyond linear state-space systems to nonlinear systems. In this work the applicability of the empirical cross gramian also for parametrized systems is demonstrated and assessed using a nonlinear benchmark problem.

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“…In [39] an extension to the classic cross Gramian is proposed. Based on results from decentralized control [16], a non-symmetric cross Gramian is computable for non-square systems and thus non-symmetric systems.…”

Section: Empirical Non-symmetric Cross Gramiansmentioning

confidence: 99%

“…For the sake of brevity, only combined state and parameter reduction is summarized here, which includes state-space reduction, parametric state-space reduction and parameter-space reduction as special cases; for an elaborate layout see [39].…”

Section: Model Reductionmentioning

confidence: 99%

“…The non-symmetric cross Gramian [39] (see Section 3.1.5) is a special variant of the cross Gramian for non-square and non-symmetric MIMO systems, which reduces to the regular cross Gramian for SISO systems. Since the computation is similar to the empirical cross Gramian and a non-symmetric variant of the empirical joint Gramian shall be computable too, instead of a Gramian type selected through the argument w, it is selectable via an option flag: Non-symmetric variants may be computed for the empirical cross Gramian (w = 'x'), empirical linear cross Gramian (w = 'y') or empirical joint Gramian (w = 'j') by activating the flag nf(7) = 1.…”

Section: Non-symmetric Cross Gramianmentioning

confidence: 99%

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emgr—The Empirical Gramian Framework

Himpe

2018

Algorithms

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System Gramian matrices are a well-known encoding for properties of input-output systems such as controllability, observability or minimality. These so-called system Gramians were developed in linear system theory for applications such as model order reduction of control systems. Empirical Gramians are an extension to the system Gramians for parametric and nonlinear systems as well as a data-driven method of computation. The empirical Gramian framework -emgrimplements the empirical Gramians in a uniform and configurable manner, with applications such as Gramian-based (nonlinear) model reduction, decentralized control, sensitivity analysis, parameter identification and combined state and parameter reduction. Keywords

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A note on the cross Gramian for non-symmetric systems

Cited by 21 publications

References 37 publications

Model reduction of discrete-time systems in limited intervals

Model reduction of discrete-time systems in limited intervals

The Empirical Cross Gramian for Parametrized Nonlinear Systems

emgr—The Empirical Gramian Framework

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