Reduced-order approximation of bilinear systems using a new hybrid method based on balanced truncation and iterative rational Krylov algorithms

Document Type : Research Article

Authors

Department of Control Engineering, Imam Khomeini International University, Qazvin, Iran.

10.24200/sci.2023.61596.7394

Abstract

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 the initial choice of the 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 ensure BIRKA convergence, two approaches, BBT and Linear BT (LBT), are applied to prepare the initial guess of the reduced-order approximation. Although BBT prepares 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 examined. Finally, the performance of the proposed approach is compared with several classical approaches. The findings indicate that the convergence probability of BIRKA increases. Also, the time for determining the Model Order Reduction (MOR) decreases.

Keywords

Main Subjects

References

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Scientia Iranica
Volume 32, Issue 15
Transactions on Computer Science & Engineering and Electrical Engineering
July and August 2025 Article ID:7394

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  • Receive Date: 18 December 2022
  • Revise Date: 23 April 2023
  • Accept Date: 15 August 2023

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