Analysis of principal component flows for general square matrices
Daiki Tsuzuki, Kentaro Ohki, "Global Convergence of Oja's Component Flow for General Square Matrices and Its Applications," (under review), 2025, arXiv
Comments: Oja flow extracts the dominant eigenspaces corresponding to the r eigenvalues of the system matrix A with the largest real parts, which is essential for continuous-time systems. Because Oja flow is an online algorithm (matrix differential equation), this result may be useful for time-varying systems.
Daiki Tsuzuki, Kentaro Ohki, "Convergence Analysis of Natural Power Method and Its Applications to Control," IFAC PapersOnline (to appear), 2026, arXiv
Comments: The natural power method extracts the dominant eigenspaces corresponding to the r eigenvalues of the system matrix A with the largest absolute values, which is essential for discrete-time systems. The natural power method is also an online algorithm, so this algorithm may be useful for time-varying cases.
For quantum systems,
Miguel Casanova, Kentaro Ohki, Francesco Ticozzi, "Quantum model reduction based on Oja's flow," (to appear), arXiv
大木健太郎, 主成分抽出アルゴリズムを用いた量子系の低次元モデル化, 第13回計測自動制御学会制御部門マルチシンポジウム予稿集, 2026
For symmetric system matrices A,
Shuto Yamada, Kentaro Ohki, "On a New Low-Rank Kalman-Bucy Filter and its Convergence Property," Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications, pp. 16-20, 2021
Shuto Yamada, Kentaro Ohki, "Comparison of estimation error between two different low-rank Kalman-Bucy filters," Proceedings of 60th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE), pp. 462-467, 2021
For general square system matrices A,
Daiki Tsuduki, Kentaro Ohki, "Low-Rank Approximated Kalman-Bucy Filters Using Oja’s Principal Component Flow for Linear Time-Invariant Systems," IEEE Control Systems Letters, vol. 8, pp. 1583-1588, 2024
Daiki Tsuduki, Kentaro Ohki, "Low-rank approximated Kalman filter using Oja's principal component flow for discrete-time linear systems," Proceedings of 2024 SICE Festival with Annual Conference (SICE FES), pp. 242-247, 2024 arXiv
Kentaro Ohki, "On the Oja-Flow-Based Low-Rank Approximation of Kalman-Bucy Filters for Linear Time-Varying Systems," (to appear in conference proceedings), 2026, arXiv