Low-Sample-Size Data-Driven Re-stabilization of Gene Network Systems

Shen, Xun; Morishita, Masahide; Imura, Jun-ichi; Oku, Makito; Aihara, Kazuyuki

doi:10.1016/j.ifacol.2022.09.353

Cited by 8 publications

(9 citation statements)

References 9 publications

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“…This paper extends the result of [23] and makes the following three main contributions: • We introduce the concept of the exact dominant pole placement, in which the dominant eigenvalue can be shifted to an arbitrary place by using the right or left dominant eigenvector;…”

Section: Key Contributions Of This Workmentioning

confidence: 84%

“…From the viewpoint of control engineering, early treatment for preventing system deterioration is essentially improving the stability degree of a high-dimensional network system [23]. The general pole placement cannot be applied to early treatment directly.…”

Section: B Related Workmentioning

confidence: 99%

“…However, the approach of [27] cannot be applied to undirected network systems. In [23] which is the preliminary conference paper of this paper, the HDSSS data-based approximate input assignment approach has been proposed for the directed networks based on Brauer theorem introduced in [28]. However, the analysis of the general performance of the approximate method in [23] must be investigated.…”

Section: B Related Workmentioning

confidence: 99%

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Model-Free Dominant Pole Placement for Restabilizing High-Dimensional Network Systems via Small-Sample-Size Data

et al. 2023

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There is a critical transition before a high-dimensional network system completely deteriorates. The Dynamical Network Marker (DNM) theory has been developed for the early prediction of such critical transitions by only using High-Dimension Small-Sample-Size (HDSSS) data. This article presents a model-free dominant pole placement approach for restabilizing the high-dimensional network systems towards avoidance of critical transitions by early treatment. Instead of traditional model-based pole placement, we present a model-free exact dominant pole placement method with dominant eigenvectors of the system matrix, which can be estimated from HDSSS data of system states. We further introduce two approximations of exact dominant pole placement to reduce the complexity of implementing restabilization. The first one is to approximate the right dominant eigenvector-based pole placement by reducing the number of intervened nodes. The second one is to intervene only in the diagonal part of the system matrix. We conduct theoretical analysis and numerical simulations to investigate the performance of the proposed dominant pole placement method.INDEX TERMS Data-driven control, matrix perturbation, pole placement. I. INTRODUCTION A. BACKGROUND AND MOTIVATION

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Section: Key Contributions Of This Workmentioning

confidence: 84%

Section: B Related Workmentioning

confidence: 99%

Section: B Related Workmentioning

confidence: 99%

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Model-Free Dominant Pole Placement for Restabilizing High-Dimensional Network Systems via Small-Sample-Size Data

et al. 2023

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“…Moreover, by substituting (26) to (13) and using (24), we obtain (14) and (15). Thus, the following holds:…”

Section: Conflict Of Interest Statementmentioning

confidence: 98%

“…Thus, the method cannot be applied to the case of HDLSS data. In a very recent study, approximate pole placement for gene network systems with HDLSS data has been proposed, 14 based on Brauer's theorem 15 . Although the method is suitable for HDLSS data, no theoretical analysis has been presented for exact characterization of the solution of the pole placement problem.…”

Section: Introductionmentioning

confidence: 99%

Design of input assignment and feedback gain for re‐stabilizing undirected networks with High‐Dimension Low‐Sample‐Size data

Yasukata

Shen

Sasahara

et al. 2023

Intl J Robust & Nonlinear

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There exists a critical transition before dramatic deterioration of a complex dynamical system. Recently, a method to predict such shifts based on High-Dimension Low-Sample-Size (HDLSS) data has been developed. Thus based on the prediction, it is important to make the system more stable by feedback control just before such critical transitions, which we call re-stabilization.However, the re-stabilization cannot be achieved by traditional stabilization methods such as pole placement method because the available HDLSS data is not enough to get a mathematical system model by system identification. In this article, a model-free pole placement method for re-stabilization is proposed to design the optimal input assignment and feedback gain for undirected network systems only with HDLSS data. The proposed method is validated by numerical simulations.

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