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Multi-level optimization with the koopman operator for data-driven, domain-aware, and dynamic system security

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  • Oster, Matthew R.
  • King, Ethan
  • Bakker, Craig
  • Bhattacharya, Arnab
  • Chatterjee, Samrat
  • Pan, Feng

Abstract

Cyber–Physical Systems (CPSs) like the power grid are critically important but also increasingly vulnerable; ensuring reliable system operation in the face of disruptions is becoming more and more challenging. Multi-Level Optimization (MLO) is a powerful way to model adversarial interactions, which naturally makes it applicable to studying CPS security. However, MLO typically does not address underlying system dynamics, and incorporating nonlinear dynamics is generally infeasible. In this paper, we show how to combine MLO with the Koopman Operator (KO) to remedy this. The KO maps nonlinear dynamics to a lifted space in which those dynamics are linear, thus making it ideal for use with MLO. Moreover, the structure of the KO also provides convenient ways to incorporate domain knowledge into the data-driven process of learning the KO representation of a given system. Our contribution is a proposed, fairly general method for incorporating nonlinear dynamics into a MLO using a learned linear representation of the KO. We also demonstrate the use and tractability of this approach through experiments on small instances of a reliability-focused power grid problem. We conclude by discussing the scalability and computational cost of this physics-informed MLO-KO approach, and identify future research directions for this work.

Suggested Citation

  • Oster, Matthew R. & King, Ethan & Bakker, Craig & Bhattacharya, Arnab & Chatterjee, Samrat & Pan, Feng, 2023. "Multi-level optimization with the koopman operator for data-driven, domain-aware, and dynamic system security," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
  • Handle: RePEc:eee:reensy:v:237:y:2023:i:c:s0951832023002375
    DOI: 10.1016/j.ress.2023.109323
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    1. Jalilpoor, Kamran & Oshnoei, Arman & Mohammadi-Ivatloo, Behnam & Anvari-Moghaddam, Amjad, 2022. "Network hardening and optimal placement of microgrids to improve transmission system resilience: A two-stage linear program," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    2. Smith, J. Cole & Song, Yongjia, 2020. "A survey of network interdiction models and algorithms," European Journal of Operational Research, Elsevier, vol. 283(3), pages 797-811.
    3. Davila-Frias, Alex & Yodo, Nita & Le, Trung & Yadav, Om Prakash, 2023. "A deep neural network and Bayesian method based framework for all-terminal network reliability estimation considering degradation," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    4. Xu, Yanwen & Kohtz, Sara & Boakye, Jessica & Gardoni, Paolo & Wang, Pingfeng, 2023. "Physics-informed machine learning for reliability and systems safety applications: State of the art and challenges," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    5. Yuan, Wei & Zhao, Long & Zeng, Bo, 2014. "Optimal power grid protection through a defender–attacker–defender model," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 83-89.
    6. Cai, Baoping & Xie, Min & Liu, Yonghong & Liu, Yiliu & Feng, Qiang, 2018. "Availability-based engineering resilience metric and its corresponding evaluation methodology," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 216-224.
    7. Shan, Xiaojun Gene & Zhuang, Jun, 2020. "A game-theoretic approach to modeling attacks and defenses of smart grids at three levels," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    8. Li, Zhanhang & Zhou, Jian & Nassif, Hani & Coit, David & Bae, Jinwoo, 2023. "Fusing physics-inferred information from stochastic model with machine learning approaches for degradation prediction," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    9. Miele, S. & Karve, P. & Mahadevan, S., 2023. "Multi-fidelity physics-informed machine learning for probabilistic damage diagnosis," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    10. Zhang, Chi & Shafieezadeh, Abdollah, 2022. "Simulation-free reliability analysis with active learning and Physics-Informed Neural Network," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    11. Steven L Brunton & Bingni W Brunton & Joshua L Proctor & J Nathan Kutz, 2016. "Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-19, February.
    12. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    13. Wang, Jing & Zuo, Wangda & Rhode-Barbarigos, Landolf & Lu, Xing & Wang, Jianhui & Lin, Yanling, 2019. "Literature review on modeling and simulation of energy infrastructures from a resilience perspective," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 360-373.
    14. Subramanian, Abhinav & Mahadevan, Sankaran, 2023. "Probabilistic physics-informed machine learning for dynamic systems," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    15. Ghorbani-Renani, Nafiseh & González, Andrés D. & Barker, Kash & Morshedlou, Nazanin, 2020. "Protection-interdiction-restoration: Tri-level optimization for enhancing interdependent network resilience," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
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