Model order reduction of linear and bilinear systems via low-rank Gramian approximation

Xiao, Zhi-Hua; Song, Qiu-Yan; Jiang, Yao‐Lin; Qi, Zhen‐Zhong

doi:10.1016/j.apm.2022.01.035

Cited by 11 publications

(1 citation statement)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The main drawback of this method was the enormous computational load for computing the Gramians of controllability and the Gramians of observability. After that, many researchers focused on MOR of bilinear systems based on the BT method and improved it [11,12]. However, the Bilinear BT (BBT) method still has disadvantages, such as high computational cost and relatively low accuracy.…”

Section: Introductionmentioning

confidence: 99%

Reduced-Order Approximation of Bilinear Systems Using a New Hybrid Method based on Balanced Truncation and Iterative Rational Krylov Algorithms

Nasiri Soloklo,

Bigdeli

2023

Scientia Iranica

View full text Add to dashboard Cite

In this work, a hybrid approach is proposed for the reduced order approximation of the bilinear system by combining the Balanced Truncation (BT) and Bilinear Iterative Rational Krylov Algorithm (BIRKA). Bilinear BT (BBT) has low accuracy but guarantees stability, while BIRKA convergence suffers from sensitivity to initial choice of reduced-order system. To start, the proposed approach minimizes the Integral Square Error (ISE) index to specify the order of the reduced bilinear approximation. To assurance BIRKA convergence, two approaches, BBT and Linear BT (LBT), are applied to prepare the initial guess of the reduced-order approximation.Although BBT prepare a good stable initial guess for BIRKA, solving the generalized Lyapunov equations to find the solution is very computationally expensive. The initial guess is provided by LBT through solving the Lyapunov equations, which decreases computational complexity. Furthermore, the eigenvalues are replaced by the condition number in BIRKA to decrease complexity. To verify the efficiency of the proposed approach, three bilinear test systems are being examined. Finally, the performance of the proposed approach is compared with several classical approaches. The finding 2 indicate that the convergence probability of BIRKA increases. Also, the time for the determining the Model Order Reduction (MOR) decreases.

show abstract

Section: Introductionmentioning

confidence: 99%

Reduced-Order Approximation of Bilinear Systems Using a New Hybrid Method based on Balanced Truncation and Iterative Rational Krylov Algorithms

Nasiri Soloklo,

Bigdeli

2023

Scientia Iranica

View full text Add to dashboard Cite

show abstract

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

Cheng,

Wang,

Miao

2024

Asian Journal of Control

View full text Add to dashboard Cite

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.

show abstract

Order Reduction of Real Time Electromechanical Systems by Using a New Model Order Reduction Method and Controller Design

Prajapati,

Sen,

Kumar

et al. 2024

Circuits Syst Signal Process

View full text Add to dashboard Cite

Model order reduction of linear and bilinear systems via low-rank Gramian approximation

Cited by 11 publications

References 28 publications

Reduced-Order Approximation of Bilinear Systems Using a New Hybrid Method based on Balanced Truncation and Iterative Rational Krylov Algorithms

Reduced-Order Approximation of Bilinear Systems Using a New Hybrid Method based on Balanced Truncation and Iterative Rational Krylov Algorithms

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

Order Reduction of Real Time Electromechanical Systems by Using a New Model Order Reduction Method and Controller Design

Contact Info

Product

Resources

About