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Volume 9 Issue 4
Apr.  2022

IEEE/CAA Journal of Automatica Sinica

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Y. H. Lin, J. W. Sun, G. Q. Li, G. X. Xiao, C. Y. Wen, L. Deng, and H. E. Stanley, “Spatiotemporal input control: Leveraging temporal variation in network dynamics,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 4, pp. 635–651, Apr. 2022. doi: 10.1109/JAS.2022.105455
Citation: Y. H. Lin, J. W. Sun, G. Q. Li, G. X. Xiao, C. Y. Wen, L. Deng, and H. E. Stanley, “Spatiotemporal input control: Leveraging temporal variation in network dynamics,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 4, pp. 635–651, Apr. 2022. doi: 10.1109/JAS.2022.105455

Spatiotemporal Input Control: Leveraging Temporal Variation in Network Dynamics

doi: 10.1109/JAS.2022.105455
Funds:  This work was partially supported by the National Key RD Program of China (2020AAA0105200, 2018AAA01012600), National Natural Science Foundation of China (61876215), Beijing Academy of Artificial Intelligence (BAAI), in part by the Science and Technology Major Project of Guangzhou (202007030006), and Pengcheng laboratory. It is also partially funded by the Ministry of Education, Singapore, under contract RG19/20, and partly supported by the Future Resilient Systems Project (FRS-II) at the Singapore-ETH Centre (SEC), funded by the National Research Foundation of Singapore (NRF)
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  • The number of available control sources is a limiting factor to many network control tasks. A lack of input sources can result in compromised controllability and/or sub-optimal network performance, as noted in engineering applications such as the smart grids. The mechanism can be explained by a linear time-invariant model, where structural controllability sets a lower bound on the number of required sources. Inspired by the ubiquity of time-varying topologies in the real world, we propose the strategy of spatiotemporal input control to overcome the source-related limit by exploiting temporal variation of the network topology. We theoretically prove that under this regime, the required number of sources can always be reduced to 2. It is further shown that the cost of control depends on two hyperparameters, the numbers of sources and intervals, in a trade-off fashion. As a demonstration, we achieve controllability over a complex network resembling the nervous system of Caenorhabditis elegans using as few as 6% of the sources predicted by a static control model. This example underlines the potential of utilizing topological variation in complex network control problems.

     

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  • Yihan Lin and Jiawei Sun contributed equally to this work.
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    Highlights

    • We show that through designing the spatiotemporal inputs, the lower bound of required sources in Controllability of complex networks [1] can be reduced. In this work, we subvert the idea by proving that via temporally switching the node-source connections, the required number of sources can be reduced to a minimum of 2, or even 1 in some special cases, and the control energy can be significantly lowered as well. At the same time, we put forward the corresponding control method.
    • We uncover that the trade-off between the minimized energy for controlling networks with spatiotemporal inputs and the two important hyper-parameters: the number of sources and the number of intervals, which is a significant and important finding regarding the previous work [2](Li et al, Science, 2017).
    • The presented methods for constructing and optimizing the input given a temporal control structure can serve as a pioneering method for designing spatiotemporal inputs and a basis for further improvement.

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