Non‐linear model‐order reduction based on tensor decomposition and matrix product

Li, Zhen; Jiang, Yao‐Lin; Xu, Kang-Li

doi:10.1049/iet-cta.2018.5264

Cited by 6 publications

(2 citation statements)

References 25 publications

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“…For bilinear systems, generally, the MOR methods for the linear systems have been extended to the bilinear system to approximate the reducedorder bilinear model. Some of the most effective ones of these methods are bilinear balanced truncation (BBT) method [14][15][16], the Krylov subspace projection methods [17][18][19][20], and the H 2 -optimal bilinear MOR methods.…”

Section: Introductionmentioning

confidence: 99%

H₂model order reduction of bilinear systems via linear matrix inequality approach

Soloklo

Bigdeli

2023

IET Control Theory & Appl

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This paper proposes an H2‐optimal model order reduction (MOR) method for bilinear systems based on the linear matrix inequality (LMI) approach. In this method, to reduce the computational complexity, at first, a reduced middle‐order approximation of the system is derived based on common bilinear MOR methods. Next, the H2 norm of the error system is minimized to obtain the reduced‐order bilinear model. Generalized Lyapunov equations are added to the optimization problem as LMI constraints to guarantee the specification of type II Gramians of the bilinear system to improve accuracy. Besides, two stability conditions are included to the optimization problem as its constraints to preserve stability of reduced‐order bilinear model. One of advantages of the proposed method is the need for only one of the Gramians of controllability or observability. Since the proposed H2‐optimal MOR problem is a polynomial matrix inequality (PMI) problem, an iterative method is used to convert the PMI to the LMI problems and solve the optimization problem. Three bilinear test systems are considered to show the proposed method's efficiency, while its performance is compared with some classical methods. Results show that the proposed methods lead to a more accurate reduced‐order model than other MOR methods.

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Section: Introductionmentioning

confidence: 99%

H₂model order reduction of bilinear systems via linear matrix inequality approach

Soloklo

Bigdeli

2023

IET Control Theory & Appl

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“…These properties are important in the engineering systems, for instance, the RLC circuit is always passive [2]. For general systems, the balanced truncation method [2, 3], the Krylov subspace method [4], the

{scriptH}_{2}

optimal approximation [5–8] and the MOR methods based on tensors [9] are efficiently used to construct reduced systems. In recent years, MOR methods of port‐Hamiltonian systems have attracted much attention.…”

Section: Introductionmentioning

confidence: 99%

Structure‐preserving interval‐limited balanced truncation reduced models for port‐Hamiltonian systems

Jiang

2020

IET Control Theory & Applications

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Parallel model order reduction methods based on structured matrix analysis for discrete-time systems with parametric uncertainty

Jiang

2023

Journal of Computational and Applied Mathematics

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Non‐linear model‐order reduction based on tensor decomposition and matrix product

Cited by 6 publications

References 25 publications

H₂model order reduction of bilinear systems via linear matrix inequality approach

H₂model order reduction of bilinear systems via linear matrix inequality approach

Structure‐preserving interval‐limited balanced truncation reduced models for port‐Hamiltonian systems

Parallel model order reduction methods based on structured matrix analysis for discrete-time systems with parametric uncertainty

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Non‐linear model‐order reduction based on tensor decomposition and matrix product

Cited by 6 publications

References 25 publications

H2model order reduction of bilinear systems via linear matrix inequality approach

H2model order reduction of bilinear systems via linear matrix inequality approach

Structure‐preserving interval‐limited balanced truncation reduced models for port‐Hamiltonian systems

Parallel model order reduction methods based on structured matrix analysis for discrete-time systems with parametric uncertainty

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H₂model order reduction of bilinear systems via linear matrix inequality approach

H₂model order reduction of bilinear systems via linear matrix inequality approach