Switched Stackelberg game analysis of false data injection attacks on networked control systems.

*(English)*Zbl 07250724Summary: This paper is concerned with a security problem for a discrete-time linear networked control system of switched dynamics. The control sequence generated by a remotely located controller is transmitted over a vulnerable communication network, where the control input may be corrupted by false data injection attacks launched by a malicious adversary. Two partially conflicted cost functions are constructed as the quantitative guidelines for both the controller and the attacker, after which a switched Stackelberg game framework is proposed to analyze the interdependent decision-making processes. A receding-horizon switched Stackelberg strategy for the controller is derived subsequently, which, together with the corresponding best response of the attacker, constitutes the switched Stackelberg equilibrium. Furthermore, the asymptotic stability of the closed-loop system under the switched Stackelberg equilibrium is guaranteed if the switching signal exhibits a certain average dwell time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method in this paper.

##### MSC:

93B70 | Networked control |

93C55 | Discrete-time control/observation systems |

93C05 | Linear systems in control theory |

91A65 | Hierarchical games (including Stackelberg games) |

91A80 | Applications of game theory |

##### Keywords:

networked control systems; false data injection attacks; switched systems; switched Stackelberg games; switched Stackelberg equilibrium
PDF
BibTeX
XML
Cite

\textit{Y. Huang} and \textit{J. Zhao}, Kybernetika 56, No. 2, 261--277 (2020; Zbl 07250724)

**OpenURL**

##### References:

[1] | Basar, T.; Olsder, G. J., Dynamic Noncooperative Game Theory., Siam, Philadelphia 1999 |

[2] | Dong, Y.; Chen, J., Finite-time outer synchronization between two complex dynamical networks with on-off coupling., Int. J. Modern Phys. C. 26 (2015), 8, 1550095 |

[3] | Ding, D.; Han, Q.-L.; Wang, Z.; Ge, X., A survey on model-based distributed control and filtering for industrial cyber-physical systems., IEEE Trans. Ind. Inf. 15 (2019), 5, 2483-2499 |

[4] | Engwerda, J., LQ Dynamic Optimization and Differential Games., John Wiley and Sons, Chichester 2005 |

[5] | Garcia, E.; Antsaklis, P., Model-based event-triggered control for systems with quantization and time-varying network delays., IEEE Trans. Automat. Control 58 (2013), 2, 422-434 |

[6] | Ge, X.; Han, Q.-L., Consensus of multiagent systems subject to partially accessible and overlapping Markovian network topologies., IEEE Trans. Cybernet. 47 (2017), 8, 1807-1819 |

[7] | Ge, X.; Han, Q.-L.; Wang, Z., A threshold-parameter-dependent approach to designing distributed event-triggered \(H_{\infty}\) consensus filters over sensor networks., IEEE Trans. Cybernet. 49 (2019), 4, 1148-1159 |

[8] | Ge, X.; Han, Q.-L.; Zhang, X.-M.; Ding, L.; Yang, F., Distributed event-triggered estimation over sensor networks: A survey., IEEE Trans. Cybernet. 50 (2019), 3, 1306-1320 |

[9] | Ge, X.; Han, Q.-L.; Zhong, M.; Zhang, X.-M., Distributed Krein space-based attack detection over sensor networks under deception attacks., Automatica 109 (2019), 108557, 108557 |

[10] | Hespanha, J. P.; Morse, A. S., Stability of switched systems with average dwell-time., In: Proc. 38th IEEE Conf. Decision Control 1999, pp. 2655-2660 |

[11] | Hu, L.; Wang, Z.; Han, Q.-L.; Liu, X., State estimation under false data injection attacks: Security analysis and system protection., Automatica 87 (2018), 176-183 |

[12] | Hu, S.; Yue, D.; Han, Q.-L.; Xie, X.; Chen, X.; Dou, C., Observer-based event-triggered control for networked linear systems subject to denial-of-service attacks., IEEE Trans. Cybernet. 50 (2019), 5, 1952-1964 |

[13] | Li, Y.; Quevedo, D. E.; Dey, S.; Shi, L., SINR-based dos attack on remote state estimation: A game-theoretic approach., IEEE Trans. Control Netw. Syst. 4 (2017), 632-642 |

[14] | Li, Y.; Shi, D.; Chen, T., False data injection attacks on networked control systems: A Stackelberg game analysis., IEEE Trans. Automat. Control 63 (2018), 3503-3509 |

[15] | Li, Y.; Shi, L.; Cheng, P.; Chen, J.; Quevedo, D. . E., Jamming attacks on remote state estimation in cyber-physical systems: A game-theoretic approach., IEEE Trans. Automat. Control 60 (2015), 2831-2836 |

[16] | Liberzon, D., Switching in Systems and Control., Birkhauser, Boston 2003 |

[17] | Liu, B.; Hill, D. J.; Sun, Z., Input-to-state-kl-stability and criteria for a class of hybrid dynamical systems., Appl. Math. Comput. 326 (2018), 124-140 |

[18] | Liu, B.; Hill, D. J.; Sun, Z., Input-to-state exponents and related iss for delayed discrete-time systems with application to impulsive effects., Int. J. Robust Nonlinear Control 28 (2018), 640-660 |

[19] | Long, L., Stabilization by forwarding design for switched feedforward systems with unstable modes., Int. J. Robust Nonlinear Control 27 (2017), 4808-4824 |

[20] | Long, L., Multiple Lyapunov functions-based small-gain theorems for switched interconnected nonlinear systems., IEEE Trans. Automat. Control 62 (2017), 3943-3958 |

[21] | Long, L.; Si, T., Small-gain technique-based adaptive nn control for switched pure-feedback nonlinear systems., IEEE Trans. Cybernet. 49 (2019), 1873-1884 |

[22] | Rubio, S. J., On coincidence of feedback Nash equilibria and Stackelberg equilibria in economic applications of differential games., J. Optim. Theory Appl. 128 (2006), 203-220 |

[23] | Sun, X.-M.; Liu, G.-P.; Rees, D.; Wang, W., Delay-dependent stability for discrete systems with large delay sequence based on switching techniques., Automatica 44 (2008), 2902-2908 |

[24] | Sun, X.-M.; Wang, W., Integral input-to-state stability for hybrid delayed systems with unstable continuous dynamics., Automatica 48 (2012), 2359-2364 |

[25] | Sun, X.; Wu, D.; Liu, G.; Wang, W., Input-to-state stability for networked predictive control with random delays in both feedback and forward channels., IEEE Trans. Ind. Electron. 61 (2014), 3519-3526 |

[26] | Sun, X.-M.; Zhao, J.; Hill, D. J., Stability and l2-gain analysis for switched delay systems: A delay-dependent method., Automatica 42 (2006), 1769-1774 |

[27] | Wang, X.; Lemmon, M., Event-triggering in distributed networked control systems., IEEE Trans. Automat. Control 56 (2011), 3, 586-601 |

[28] | Wu, J.; Chen, T., Design of networked control systems with packet dropouts., IEEE Trans. Automat. Control 52 (2007), 1314-1319 |

[29] | Xiao, S.; Han, Q.-L.; Ge, X.; Zhang, Y., Secure distributed finite-time filtering for positive systems over sensor networks under deception attacks., IEEE Trans. Cybernet. 50 (2019), 3, 1220-1229 |

[30] | Xu, X.; Antsaklis, P. J., Optimal control of switched systems based on parameterization of the switching instants., IEEE Trans. Automat. Control 49 (2004), 2-16 |

[31] | You, K.; Li, Z.; Xie, L., Consensus condition for linear multi-agent systems over randomly switching topologies., Automatica 49 (2013), 10, 3125-3132 |

[32] | Zhang, L.; Gao, H.; Kaynak, O., Network-induced constraints in networked control systems - A survey., IEEE Trans. Ind. Inf. 9 (2013), 1, 403-416 |

[33] | Zhang, X.-M.; Han, Q.-L.; Yu, X., Survey on recent advances in networked control systems., IEEE Trans. Ind. Inf. 12 (2016), 5, 1740-1752 |

[34] | Zhang, Y.; Tian, Y.-P., Consentability and protocol design of multi-agent systems with stochastic switching topology., Automatica 45 (2009), 5, 1195-1201 |

[35] | Zhao, J.; Hill, D. J., Dissipativity theory for switched systems., IEEE Trans. Automat. Control 53 (2008), 941-953 |

[36] | Zhao, J.; Hill, D. J.; Liu, T., tability of dynamical networks with non-identical nodes: A multiple \(V\)-Lyapunov function method., Automatica 47 (2011), 2615-2625 |

[37] | Zhu, M.; MartĂnez, S., Stackelberg-game analysis of correlated attacks in cyber-physical systems., In: Proc. Amer. Control Conf. 2011, pp. 4063-4068 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.