Zero-Sum Game-Based Optimal Secure Control Under Actuator Attacks

• Published in: IEEE transactions on automatic control Vol. 66; no. 8; pp. 3773 - 3780
• Main Authors: Wu, Chengwei, Li, Xiaolei, Pan, Wei, Liu, Jianxing, Wu, Ligang
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Attack; Cost function; Cyber-physical systems; cyber–physical systems (CPS); Dynamic programming; Estimation; Game theory; Games; Kalman filters; Noise measurement; Robot sensing systems; secure control; Symmetric matrices; System performance; Zero sum games; zero-sum game
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2020.3029342

This article investigates the zero-sum game-based secure control problem for cyber-physical systems (CPS) under the actuator false data injection attacks. The physical process is described as a linear time-invariant discrete-time model. Both the process noise and the measurement noise are addressed in the design process. An optimal Kalman filter is given to estimate the system states. The adversary and the defender are modeled as two players. Under the zero-sum game framework, an optimal infinite-horizon quadratic cost function is defined. Employing the dynamic programming approach, the optimal defending policy and the attack policy are derived. The convergence of the cost function is proved. Moreover, the critical attack probability is derived, beyond which the cost cannot be bounded. Finally, simulation results are provided to validate the proposed secure scheme.