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Controlling complex networks with complex nodes

Nature Reviews Physics volume 5, pages 250–262 (2023)Cite this article

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Abstract

Real-world networks often consist of millions of heterogenous elements that interact at multiple timescales and length scales. The fields of statistical physics and control theory both contribute different perspectives for understanding, modelling and controlling these systems. To address real-world systems, more interaction between these fields and integration of new paradigms such as heterogeneity and multiple levels of representation will be necessary. It may be possible to expand models from statistical physics to integrate the notion of feedback (both positive and negative) and to extend control theory formulations to more mesoscopic analysis over averages of collections of degrees of freedom. There is also the need to integrate theoretical models, machine learning and data-driven control methods. We review recent progress and identify opportunities to help advance understanding and control of real-world systems from oscillator networks and social networks to biological and technological networks.

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Fig. 1: Common elements found in complex networks.
Fig. 2: Identification of driver nodes and phase transition in the structural control framework.
Fig. 3: Control paradigms.
Fig. 4: Closing the feedback loop in complex networks entails sensing, computing and actuating at different scales.
Fig. 5: Main stages of a classical closed-loop controller design.

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Acknowledgements

The authors thank all the participants of the Satellite Symposium on ‘Controlling Complex Networks’ held at the International School and Conference on Network Science (NetSci) 2014, 2015, 2016, 2017, 2018, 2019 and 2021 and all the participants in the focus group on control held at the Future Directions in Network Science meeting in 2016 for very stimulating discussions that have helped shape our understanding. The authors also thank M. Coraggio, G. Maffettone and D. Salzano from the University of Naples Federico II, Italy and the Scuola Superiore Meridionale, Naples for their help in generating Figs. 3–5. The authors also thank A. Aparicio, C. Chen and X.-W. Wang and G. Mikaberidze for their comments on the manuscript.

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Authors and Affiliations

  1. Department of Computer Science and Department of Mechanical and Aerospace Engineering, University of California, Davis, CA, USA

    Raissa M. D’Souza

  2. Santa Fe Institute, Santa Fe, NM, USA

    Raissa M. D’Souza

  3. Complexity Sciences Hub Vienna, Vienna, Austria

    Raissa M. D’Souza

  4. Department of Electric Engineering and Information Technology, University of Naples Federico II, Naples, Italy

    Mario di Bernardo

  5. Scuola Superiore Meridionale, Naples, Italy

    Mario di Bernardo

  6. Channing Division of Network Medicine, Department of Medicine, Brigham and Women’s Hospital and Harvard Medical School, Boston, MA, USA

    Yang-Yu Liu

  7. Center for Artificial Intelligence and Modelling, The Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Yang-Yu Liu

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D’Souza, R.M., di Bernardo, M. & Liu, YY. Controlling complex networks with complex nodes. Nat Rev Phys 5, 250–262 (2023). https://doi.org/10.1038/s42254-023-00566-3

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