Cross-Gramian-Based Model Reduction: A Comparison

Himpe, Christian; Ohlberger, Mario

doi:10.1007/978-3-319-58786-8_17

Cited by 5 publications

(4 citation statements)

References 24 publications

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“…Expanding the matrix description (31) into four submatrix equations, we arrive at Eqns. (27) to (30). This completes the proof.…”

Section: Lemmasupporting

confidence: 63%

“…Various methods can be used to obtain projection matrices from the cross Gramian [4,5,9,27,57]. The first approach can be performed on the basis of singular value decomposition (SVD) of the cross Gramian…”

Section: Cross Gramian-based Model Order Reductionmentioning

confidence: 99%

“…This concept was firstly introduced for single-input single-output (SISO) and symmetric multi-input multi-output (MIMO) systems [17,18,39]. Furthermore, this approach was also extended to nonlinear systems by the use of empirical Gramians [13,24,27].…”

Section: Introductionmentioning

confidence: 99%

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New integer-order approximations of discrete-time non-commensurate fractional-order systems using the cross Gramian

Rydel

2018

Adv Comput Math

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This paper presents a new approach to modeling of linear time-invariant discrete-time non-commensurate fractional-order single-input single-output state space systems by means of the Balanced Truncation and Frequency Weighted model order reduction methods based on the cross Gramian. These reduction methods are applied to the specific rational (integer-order) FIR-based approximation to the fractional-order system, which enables to introduce simple, analytical formulae for determination of the cross Gramian of the system. This leads to significant decrease of computational burden in the reduction algorithm. As a result, a rational and relatively low-order state space approximator for the fractional-order system is obtained. A simulation experiment illustrates an efficiency of the introduced methodology in terms of high approximation accuracy and low time complexity of the proposed method.

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“…Expanding the matrix description (31) into four submatrix equations, we arrive at Eqns. (27) to (30). This completes the proof.…”

Section: Lemmasupporting

confidence: 63%

Section: Cross Gramian-based Model Order Reductionmentioning

confidence: 99%

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New integer-order approximations of discrete-time non-commensurate fractional-order systems using the cross Gramian

Rydel

2018

Adv Comput Math

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“…The first example is a linear test system of the form (2) and generated using the inverse Lyapunov procedure [85], in a variant that enforces state-space symmetric systems [43]. For state-space symmetric systems, A = A , B = C , all system Gramians are symmetric and equal [58].…”

Section: Linear Verificationmentioning

confidence: 99%

Emgr - Empirical Gramian Framework (5.4)

Himpe

2018

Self Cite

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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 Gramian are an extension to the system Gramians for parametric and nonlinear systems as well as a data-driven method of computation. The empirical Gramian frameworkemgr -implements 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.

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