大規模なネットワークの障害は、ローカルに焦点を当てることで防ぐことができる(Failures in large networks can be prevented with local focus)

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大規模で複雑なネットワークの制御という課題に応える新手法 New method addresses challenge of controlling large complex networks

2022-08-08 ノースウェスタン大学


In their study, the researchers demonstrate the effectiveness of their method through four concrete examples, including the stability control of the Eastern U.S. power grid.

研究チームは、複雑なネットワークが持つユビキタスな性質を発見し、その性質を体系的に利用して、局所的な情報のみを用いてネットワーク全体を制御する新しい計算手法を初めて開発しました。この方法は、計算時間と情報通信コストを考慮して最適な選択を導き出すものです。
研究者らは今回の研究で、世界的な航空輸送ネットワークを通じた伝染病の蔓延の抑制や、米国東部の電力網の安定制御など、4つの具体例を通じて、この手法の有効性を実証しています。
新しい手法の鍵は、研究者が実際のネットワークにおけるダイナミクスのこの非線形性を考慮したことです。このようなシステムでは、一般に、応答の大きさと外乱の大きさは比例しない。

<関連情報>

局所的なネットワークの普及とスケーラブルな制御 Prevalence and scalable control of localized networks

Chao Duan , Takashi Nishikawa  and Adilson E. Motter
Proceedings of the National Academy of Sciences  Published:August 5, 2022
DOI:https://doi.org/10.1073/pnas.2122566119

Significance

The control of large-scale networks is a pressing problem of relevance to numerous natural and engineered systems. Despite recent advances in network and control science, there has been a lack of fundamental understanding about the network properties that can enable effective and efficient control of such systems. Here, we demonstrate that network locality, which we show to be a rather common property, can dramatically improve our ability to control large-scale networks. In particular, we demonstrate that locality can be exploited to substantially simplify the task of controlling nonlinear networks for desirable dynamical performance while minimizing the control effort. Our theory and algorithms provide a unified framework and show that local computation and communication suffice to achieve near-optimal control outcomes.

Abstract

The ability to control network dynamics is essential for ensuring desirable functionality of many technological, biological, and social systems. Such systems often consist of a large number of network elements, and controlling large-scale networks remains challenging because the computation and communication requirements increase prohibitively fast with network size. Here, we introduce a notion of network locality that can be exploited to make the control of networks scalable, even when the dynamics are nonlinear. We show that network locality is captured by an information metric and is almost universally observed across real and model networks. In localized networks, the optimal control actions and system responses are both shown to be necessarily concentrated in small neighborhoods induced by the information metric. This allows us to develop localized algorithms for determining network controllability and optimizing the placement of driver nodes. This also allows us to develop a localized algorithm for designing local feedback controllers that approach the performance of the corresponding best global controllers, while incurring a computational cost orders-of-magnitude lower. We validate the locality, performance, and efficiency of the algorithms in Kuramoto oscillator networks, as well as three large empirical networks: synchronization dynamics in the Eastern US power grid, epidemic spreading mediated by the global air-transportation network, and Alzheimer’s disease dynamics in a human brain network. Taken together, our results establish that large networks can be controlled with computation and communication costs comparable to those for small networks.

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