Laguerre functions approximation for model reduction of second order time-delay systems

Wang, Xiaolong; Jiang, Yao‐Lin; Kong, Xu

doi:10.1016/j.jfranklin.2016.06.024

Cited by 19 publications

(8 citation statements)

References 41 publications

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“…In this section, the proposed method is validated by three examples, which are conducted by using MATLAB and all the examples are performed on DELL TOWER 7910 processor. The proposed method is compared with the two‐sided Laguerre‐based MOR method in [24]. Orig S, Red S‐1 and Red S‐2 denote the original system, the reduced system obtained by the Laguerre‐based MOR method and the reduced system obtained by the proposed method, respectively.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…We reduce the second‐order TDS to

r = 45

. In order to obtain Red S‐1, the parameter

α

in [24] is set as

α = 24.5

. The numbers of the samples in thefrequency range

false[10^{- 1}, 10^{2} false]

are taken as

m = 70

, 80 and 90, respectively.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Considering the frequency range

false[10^{- 4}, 10 false]

, the numbers of the samples are

m = 60

and 80, respectively. The parameter

α

in [24] is set as

α = 0.05

. We also generate Red S‐2 by directly usingAlgorithm 1 to the original system and the number of samples are

m = 70

.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The multiorder Arnoldi approach was applied to second‐order TDSs, and Xiao and Jiang [23] proved that the transfer function of the reduced model can match a certain number of approximate moments or Laguerre expansion coefficients. In addition, Wang , et al [24] adopted the Laguerre expansion for time‐delay elements and proved that the Laguerre coefficients satisfied a linear system and can be computed iteratively.…”

Section: Introductionmentioning

confidence: 99%

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Structure preserving model reduction of second‐order time‐delay systems via approximate Gramians

Jiang

Qiu

Yang

2020

IET Circuits, Devices & Systems

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In this study, a model-order reduction approach based on approximate Gramians for second-order time-delay systems is proposed. By treating the second-order time-delay system as a special case of the integro-differential system, it exhibits a connection with the time-delay Gramians of the corresponding first-order system. After applying the approximate Gramians and balanced truncation procedures, the resulting reduced system is expected to well approximate the original system. Besides, the ε-embedding technique is applied to the case when the damping matrix of the second-order time-delay system is singular. Finally, numerical examples show the good performance in the time domain and the finite frequency range.

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Section: Numerical Resultsmentioning

confidence: 99%

“…We reduce the second‐order TDS to

r = 45

. In order to obtain Red S‐1, the parameter

α

in [24] is set as

α = 24.5

. The numbers of the samples in thefrequency range

false[10^{- 1}, 10^{2} false]

are taken as

m = 70

, 80 and 90, respectively.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Considering the frequency range

false[10^{- 4}, 10 false]

, the numbers of the samples are

m = 60

and 80, respectively. The parameter

α

in [24] is set as

α = 0.05

. We also generate Red S‐2 by directly usingAlgorithm 1 to the original system and the number of samples are

m = 70

.…”

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Structure preserving model reduction of second‐order time‐delay systems via approximate Gramians

Jiang

Qiu

Yang

2020

IET Circuits, Devices & Systems

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show abstract

“…It generates a much smaller system to approximate the original system such that the small system can retain some important properties (Jiang, 2010). Up to now, a lot of model reduction methods have emerged, such as Krylov subspace methods (Villemagne and Skelton, 1987; Yuan and Jiang, 2017), polynomials-based model reduction methods (Jiang and Chen, 2012; Kumar et al, 2016; Wang et al, 2016) and H 2 optimal model reduction methods (Qiu et al, 2018; Van Dooren et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

Truncated model reduction methods for linear time-invariant systems via eigenvalue computation

Yang

Jiang

2020

Transactions of the Institute of Measurement and Control

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This paper provides three model reduction methods for linear time-invariant systems in the view of the Riemannian Newton method and the Jacobi-Davidson method. First, the computation of Hankel singular values is converted into the linear eigenproblem by the similarity transformation. The Riemannian Newton method is used to establish the model reduction method. Besides, we introduce the Jacobi-Davidson method with the block version for the linear eigenproblem and present the corresponding model reduction method, which can be seen as an acceleration of the former method. Both the resulting reduced systems can be equivalent to the reduced system originating from a balancing transformation. Then, the computation of Hankel singular values is transformed into the generalized eigenproblem. The Jacobi-Davidson method is employed to establish the model reduction method, which can also lead to the reduced system equivalent to that resulting from a balancing transformation. This method can also be regarded as an acceleration of a Riemannian Newton method. Moreover, the application for model reduction of nonlinear systems with inhomogeneous conditions is also investigated.

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Special structural Gramian approximation methods for model order reduction of time‐delay systems

Cheng,

Wang,

Miao

2024

Asian Journal of Control

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Model order reduction methods via low‐rank approximation of Gramians for time‐delay systems are developed in this paper. The main contribution is to achieve the balancing and truncation of the system by utilizing low‐rank decomposition of the Gramians combined with the low‐rank square root framework. Here, based on Laguerre expansion technique, the low‐rank factorization of the system Gramians is realized via a linear system with special structure, thus enabling an efficient implementation of the reduction process. Furthermore, the issue of stability preservation is briefly described. We employ the dominant subspaces projection model reduction method to mitigate the effects which may accidentally produce unstable reduced models. Finally, numerical results verify the performance of the approximation‐Gramian methods.

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Laguerre functions approximation for model reduction of second order time-delay systems

Cited by 19 publications

References 41 publications

Structure preserving model reduction of second‐order time‐delay systems via approximate Gramians

Structure preserving model reduction of second‐order time‐delay systems via approximate Gramians

Truncated model reduction methods for linear time-invariant systems via eigenvalue computation

Special structural Gramian approximation methods for model order reduction of time‐delay systems

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