Optimal joint control and triggering strategies against denial of service attacks: a zero-sum game

Optimal joint control and triggering strategies against denial of service attacks: a zero-sum game

For access to this article, please select a purchase option:

Buy article PDF
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Your details
Why are you recommending this title?
Select reason:
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

This study is concerned with the optimal control and scheduling problem for linear networked control systems with communication constraints and security issues. The communication channel, which connects remote sensors with a controller, has limited transmission capability and may suffer denial of service attacks from an external attacker. Unlike most existing cyber-attack-related literature which presumed a prior well-designed control or estimating strategy on which triggering and jamming strategies were established, in the present work, optimal strategies of the controller, the trigger as well as the external attacker are considered simultaneously under the renowned linear quadratic criteria. A designer, who can jointly devise the controller and the trigger, aims to improve the system's performance while the attacker's goal is just the opposite. With the assumption that the trigger and the attacker have limited opportunities to send or attack, a zero-sum static game of complete information is first utilised to investigate the optimal strategies for both players, i.e. the designer and the attacker. The existence of Nash equilibrium (NE) point, i.e. the combination of optimal strategy for each player, is proven afterwards. Finally, the property of none pure-strategy NE in a special case is provided with rigorous proofs. A numerical example is employed to demonstrate how to derive the optimal strategies for the designer and the attacker.


    1. 1)
      • 1. Zhang, L., Gao, H., Kaynak, O.: ‘Network-induced constraints in networked control systems — a survey’, IEEE Trans. Ind. Inf., 2013, 9, (1), pp. 403416.
    2. 2)
      • 2. Li, W., Zhu, Z., Ding, S.X.: ‘Fault detection design of networked control systems’, IET Control Theory Appl., 2011, 5, (12), pp. 14391449.
    3. 3)
      • 3. Li, H., Chow, M.Y., Sun, Z.: ‘State feedback stabilisation of networked control systems’, IET Control Theory Appl., 2009, 3, (7), pp. 929940.
    4. 4)
      • 4. Zhang, H., Cheng, P., Shi, L., et al: ‘Optimal denial-of-service attack scheduling with energy constraint’, IEEE Trans. Autom. Control, 2015, 60, (11), pp. 30233028.
    5. 5)
      • 5. Colandairaj, J., Irwin, G.W., Scanlon, W.G.: ‘Wireless networked control systems with QoS-based sampling’, IET Control Theory Appl., 2007, 1, (1), pp. 430438.
    6. 6)
      • 6. Sahu, S.S., Pandey, M.: ‘Distributed denial of service attacks: a review’, Int. J. Mod. Educ. Comput. Sci., 2014, 6, (1), pp. 6571.
    7. 7)
      • 7. Zargar, S.T., Joshi, J., Tipper, D.: ‘A survey of defense mechanisms against distributed denial of service (DDoS) flooding attacks’, IEEE Commun. Surv. Tutor., 2013, 15, (4), pp. 20462069.
    8. 8)
      • 8. Jia, H.M., Yang, Z.W., Song, W.L.: ‘Cubature Kalman filter estimation algorithm with state constraints’, J. Shandong Univ. Sci. Technol., 2015, 34, (161), pp. 8489.
    9. 9)
      • 9. Meng, X.J., Jin, H.F., Qiu, C.Y.: ‘Design and implementation of distributed network-based intrusion detection system’, J. Shandong Univ. Sci. Technol., 2003, 22, (3), pp. 3941.
    10. 10)
      • 10. Amin, S., Cardenas, A.A., Sastry, S.S.: ‘Safe and secure networked control systems under denial-of-service attacks’. Int. Workshop on Hybrid Systems Computation and Control, Heidelberg, Germany, April 2009, pp. 3145.
    11. 11)
      • 11. Zuba, M., Shi, Z., Peng, Z., et al: ‘Launching denial-of-service jamming attacks in underwater sensor networks’. Proc. of the Sixth ACM Int. Workshop on Underwater Networks, Seattle, USA, December 2011, pp. 12:112:5.
    12. 12)
      • 12. Roy, S., Ellis, C., Shiva, S., et al: ‘A survey of game theory as applied to network security’. 43rd Hawaii Int. Conf. on System Sciences, Honolulu, USA, January 2010, pp. 110.
    13. 13)
      • 13. Li, H., Lai, L., Qiu, R.C.: ‘A denial-of-service jamming game for remote state monitoring in smart grid’. 45th Annual Conf. on Information Sciences and Systems, Baltimore, USA, March 2011, pp. 16.
    14. 14)
      • 14. Gupta, A., Nayyar, A., Langbort, C., et al: ‘A dynamic transmitter-jammer game with asymmetric information’. 51st IEEE Conf. on Decision and Control, Maui, USA, December 2012, pp. 64776482.
    15. 15)
      • 15. Li, Y., Shi, L., Cheng, P., et al: ‘Jamming attacks on remote state estimation in cyber-physical systems: a game-theoretic approach’, IEEE Trans. Autom. Control, 2015, 60, (10), pp. 28312836.
    16. 16)
      • 16. Borrelli, F., Keviczky, T.: ‘Distributed LQR design for identical dynamically decoupled systems’, IEEE Trans. Autom. Control, 2008, 53, (8), pp. 19011912.
    17. 17)
      • 17. Cao, Y., Ren, W.: ‘Optimal linear-consensus algorithms: an LQR perspective’, IEEE Trans. Syst. Man Cybern. B, Cybern., 2010, 40, (3), pp. 819830.
    18. 18)
      • 18. Ramesh, C., Sandberg, H., Bao, L., et al: ‘On the dual effect in state-based scheduling of networked control systems’. Proc. of the 2011 American Control Conf., San Francisco, USA, June 2011, pp. 22162221.
    19. 19)
      • 19. Molin, A., Hirche, S.: ‘On LQG joint optimal scheduling and control under communication constraints’. Proc. of the 48th IEEE Conf. on Decision and Control, Shanghai, China, December 2009, pp. 58325838.
    20. 20)
      • 20. Shi, L., Yuan, Y., Chen, J.: ‘Finite horizon LQR control with limited controller-system communication’, IEEE Trans. Autom. Control, 2013, 58, (7), pp. 18351841.
    21. 21)
      • 21. He, X., Wang, Z., Qin, L., et al: ‘Active fault-tolerant control for an internet-based networked three-tank system’, IEEE Trans. Control Syst. Technol., 2016, 24, (6), pp. 21502157.
    22. 22)
      • 22. Raffo, G.V., Ortega, M.G., Rubio, F.R.: ‘An integral predictive/nonlinear H control structure for a quadrotor helicopter’, Automatica, 2010, 46, (1), pp. 2939.
    23. 23)
      • 23. Molin, A., Hirche, S.: ‘On the optimality of certainty equivalence for event-triggered control systems’, IEEE Trans. Autom. Control, 2013, 58, (2), pp. 470474.
    24. 24)
      • 24. Mahmoud, M.S., Memon, A.M.: ‘Aperiodic triggering mechanisms for networked control systems’, Inf. Sci., 2015, 296, pp. 282306.
    25. 25)
      • 25. Manshaei, M.H., Zhu, Q., Alpcan, T., et al: ‘Game theory meets network security and privacy’, ACM Comput. Surv. (CSUR), 2013, 45, (3), pp. 25:125:39.
    26. 26)
      • 26. Gupta, A., Langbort, C., Basar, T.: ‘Optimal control in the presence of an intelligent jammer with limited actions’. 49th IEEE Conf. on Decision and Control, Atlanta, GA, December 2010, pp. 10961101.
    27. 27)
      • 27. Miao, F., Pajic, M., Pappas, G.J.: ‘Stochastic game approach for replay attack detection’. 52nd IEEE Conf. on Decision and Control, Firenze, Italy, December 2013, pp. 18541859.
    28. 28)
      • 28. Teixeira, A., Shames, I., Sandberg, H., et al: ‘A secure control framework for resource-limited adversaries’, Automatica, 2015, 51, pp. 135148.
    29. 29)
      • 29. Chen, Y., Kar, S., Moura, J.M.: ‘Dynamic attack detection in cyber-physical systems with side initial state information’, IEEE Trans. Autom. Control, 2016, PP, 99, p. 1doi: 10.1109/TAC.2016.2626267.
    30. 30)
      • 30. Falliere, N., Murchu, L.O., Chien, E.: ‘W32. Stuxnet Dossier’ (Symantec Corp, 2011), pp. 168.
    31. 31)
      • 31. Fudenberg, D., Tirole, J.: ‘Game theory’ (MIT Press, 1991).
    32. 32)
      • 32. Bertsekas, D.P.: ‘Dynamic programming and optimal control’ (Athena Scientific Press, 1995).
    33. 33)
      • 33. Astrom, K.J.: ‘Introduction to stochastic control theory’ (Academic Press, 1970).
    34. 34)
      • 34. Lunze, J.: ‘Control theory of digitally networked dynamic systems’ (Springer Press, 2014).
    35. 35)
      • 35. Wooldridge, J.M.: ‘Econometric analysis of cross section and panel data’ (MIT Press, 2010).
    36. 36)
      • 36. Nash, J.F.: ‘Equilibrium points in n-person games’. Proc. of the National Academy of Sciences, USA, January 1950, pp. 4849.
    37. 37)
      • 37. Dixit, A.K., Skeath, S.: ‘Games of strategy’ (WW NORTON Press, 2004).

Related content

This is a required field
Please enter a valid email address