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Whittle’s Index Based Sensor Scheduling for Multiprocess Systems Under DoS Attacks

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Abstract

In this paper, the authors consider how to design defensive countermeasures against DoS attacks for remote state estimation of multiprocess systems. For each system, a sensor will measure its state and transmits the data packets through an unreliable channel which is vulnerable to be jammed by an attacker. Under limited communication bandwidth, only a subset of sensors are allowed for data transmission, and how to select the optimal one to maximize the accuracy of remote state estimation is the focus of the proposed work. The authors first formulate this problem as a Markov decision process and investigate the existence of optimal policy. Moreover, the authors demonstrate the piecewise monotonicity structure of optimal policy. Given the difficulty of obtaining an optimal policy of large-scale problems, the authors develop a suboptimal heuristic policy based on the aforementioned policy structure and Whittle’s index. Moreover, a closed form of the indices is derived in order to reduce implementation complexity of proposed scheduling policy and numerical examples are provided to illustrate the proposed developed results.

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References

  1. Sha L, Gopalakrishnan S, Liu X, et al., Cyber-physical systems: A new frontier, 2008 IEEE International Conference on Sensor Networks, Ubiquitous, and Trustworthy Computing (SUTC 2008), Taichung, 2008.

  2. Rajkumar R, Lee I, Sha L, et al., Cyber-physical systems: The next computing revolution, Proceedings of the 47th Design Automation Conference, Anaheim, 2010.

  3. Lee E A, Cyber physical systems: Design challenges, 2008 11th IEEE International Symposium on Object and Component-Oriented Real-Time Distributed Computing (ISORC), Orlando, 2008.

  4. Dibaji S M, Pirani M, Flamholz D B, et al., A systems and control perspective of CPS security, Annual Reviews in Control, 2019, 47: 394–411.

    Article  MathSciNet  Google Scholar 

  5. Sinopoli B, Schenato L, Franceschetti M, et al., Kalman filtering with intermittent observations, IEEE Trans. on Automatic Control, 2004, 49(9): 1453–1464.

    Article  MathSciNet  Google Scholar 

  6. Kuvshinkova S, SQL Slammer worm lessons learned for consideration by the electricity sector, North American Electric Reliability Council, 2003, 1(2): 5.

    Google Scholar 

  7. Chen T M and Abu-Nimeh S, Lessons from stuxnet, Computer, 2011, 44(4): 91–93.

    Article  Google Scholar 

  8. Peng T, Leckie C, and Ramamohanarao K, Survey of network-based defense mechanisms countering the DoS and DDoS problems, ACM Computing Surveys (CSUR), 2007, 39(1): 3.

    Article  Google Scholar 

  9. Wu G Y and Sun J, Optimal data integrity attack on actuators in cyber-physical systems, 2016 American Control Conference (ACC), Boston, 2016.

  10. Guo Z, Shi D, Johansson K H, et al., Optimal linear cyber-attack on remote state estimation, IEEE Trans. Control of Network Systems, 2017, 4(1): 4–13.

    Article  MathSciNet  Google Scholar 

  11. Zhang H, Cheng P, Shi L, et al., Optimal denial-of-service attack scheduling with energy constraint, IEEE Trans. Automatic Control, 2015, 60(11): 3023–3028.

    Article  MathSciNet  Google Scholar 

  12. Gao R, Huang J, and Wang L, Leaderless consensus control of uncertain multi-agents systems with sensor and actuator attacks, Information Sciences, 2019, 505: 144–156.

    Article  MathSciNet  Google Scholar 

  13. Chen Y, Kar S, and Moura J M F, Resilient distributed estimation: Sensor attacks, IEEE Trans. Automatic Control, 2018, 64(9): 3772–3779.

    Article  MathSciNet  Google Scholar 

  14. Ma R, Shi P, and Wu L, Dissipativity-based sliding-mode control of cyber-physical systems under denial-of-service attacks, IEEE Trans. Cybernetics, 2020, 51(5): 2306–2318.

    Article  Google Scholar 

  15. Feng S, Cetinkaya A, Ishii H, et al., Networked control under DoS attacks: Tradeoffs between resilience and data rate, IEEE Trans. Automatic Control, 2020, 66(1): 460–467.

    Article  MathSciNet  Google Scholar 

  16. Li Y, Shi L, Cheng P, et al., Jamming attacks on remote state estimation in cyber-physical systems: A game-theoretic approach, IEEE Trans. Automatic Control, 2015, 60(10): 2831–2836.

    Article  MathSciNet  Google Scholar 

  17. Ding K, Li Y, Quevedo D E, et al., A multi-channel transmission schedule for remote state estimation under DoS attacks, Automatica, 2017, 78: 194–201.

    Article  MathSciNet  Google Scholar 

  18. Nisan N, Roughgarden T, and Tardos E, Algorithmic Game Theory, Cambridge University Press, Cambridge, 2007.

    Book  Google Scholar 

  19. Wu S, Ding K, Cheng P, et al., Optimal scheduling of multiple sensors over lossy and bandwidth limited channels, IEEE Trans. Control of Network Systems, 2020, 7(3): 1188–1200.

    Article  MathSciNet  Google Scholar 

  20. Ren X, Wu J, Dey S, et al., Attack allocation on remote state estimation in multi-systems: Structural results and asymptotic solution, Automatica, 2018, 87: 184–194.

    Article  MathSciNet  Google Scholar 

  21. Kalman R E, A new approach to linear filtering and prediction problems, Transactions of the ASME-Hournal of Basic Engineering, 1960, 82: 35–45.

    Article  MathSciNet  Google Scholar 

  22. Mo Y, Chabukswar R, and Sinopoli B, Detecting integrity attacks on SCADA systems, IEEE Trans. Control Systems Technology, 2013, 22(4): 1396–1407.

    Google Scholar 

  23. Anderson B D O and Moore J B, Optimal Filtering, Courier Corporation, North Chelmsford, 2012.

    Google Scholar 

  24. Shi L and Zhang H, Scheduling two gauss-markov systems: An optimal solution for remote state estimation under bandwidth constraint, IEEE Trans. Signal Processing, 2012, 60(4): 2038–2042.

    Article  ADS  MathSciNet  Google Scholar 

  25. Mesquita A R, Hespanha J P, and Nair G N, Redundant data transmission in control/estimation over lossy networks, Automatica, 2012, 48(8): 1612–1620.

    Article  MathSciNet  Google Scholar 

  26. Whittle P, Restless bandits: Activity allocation in a changing world, Journal of Applied Probability, 1988, 25(A): 287–298.

    Article  MathSciNet  Google Scholar 

  27. Kailath T, Sayed A H, and Hassibi B, Linear Estimation, Prentice Hall, Hoboken, 2000.

    Google Scholar 

  28. Hernández-Lerma O and Lasserre J B, Discrete-Time Markov Control Processes: Basic Optimality Criteria, Springer Science & Business Media, New York, 2012.

    Google Scholar 

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Correspondence to Kemi Ding.

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The authors declare no conflict of interest.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 20231120102304001, STIC under Grant Nos. 62303212 and ZDSYS20220330161800001.

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Cai, Z., Ding, K. Whittle’s Index Based Sensor Scheduling for Multiprocess Systems Under DoS Attacks. J Syst Sci Complex 37, 329–350 (2024). https://doi.org/10.1007/s11424-024-3450-3

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  • DOI: https://doi.org/10.1007/s11424-024-3450-3

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