Finite-horizon semi-Markov game for time-sensitive attack response and probabilistic risk assessment in nuclear power plants

Yunfei Zhao, Linan Huang, Carol Smidts, Quanyan Zhu

Research output: Contribution to journalArticlepeer-review


Cybersecurity has drawn increasing attention in the nuclear industry. To improve the cyber-security posture, it is important to develop effective methods for cyber-attack response and cyber-security risk assessment. In this research, we develop a finite-horizon semi-Markov general-sum game between the defender (i.e., plant operator) and the attacker to obtain the time-sensitive attack response strategy and the real-time risk assessment in nuclear power plants. We propose methods for identifying system states of concern to reduce the state space and for determining state transition probabilities by integrating Probabilistic Risk Assessment techniques. After a proper discretization of the developed continuous-time model, we use dynamic programming to derive the time-varying and state-dependent strategy of the defender based on the solution concept of the mixed-strategy Nash equilibrium. For risk assessment, three risk metrics are considered, and an exact analytical algorithm and a Monte Carlo simulation-based algorithm for obtaining the metrics are developed. Both players’ strategies and the risk metrics are illustrated using a digital feedwater control system used in pressurized water reactors. The results show that the proposed method can support plant operators in timely cyber-attack response and effective risk assessment, reduce the risk, and improve the resilience of nuclear power plants to malicious cyber-attacks.

Original languageEnglish (US)
Article number106878
JournalReliability Engineering and System Safety
StatePublished - Sep 2020


  • Cyber-attack response
  • Dynamic programming
  • Feedwater control system
  • Game theory
  • Non-stationary strategy
  • Nuclear power plant
  • Probabilistic risk assessment
  • Semi-Markov decision process

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Industrial and Manufacturing Engineering


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