Optimal collaborative multiple attack strategy under the energy constraint in cyber-physical systems

Jing Bai, Yi-Gang Li, Xiu-Xiu Ren and Xuan Liu

International Journal of Systems Science, 2026, vol. 57, issue 2, 511-528

Abstract: This study proposes the collaborative multiple attack strategy in cyber-physical systems (CPSs) under the energy constraint. Distinct from the relevant studies which only consider deception attacks or denial-of-service (DoS) attacks, the collaborative design of false data injection (FDI) attacks and DoS attacks is investigated, which is more general in the practical scenarios. The duration times for two types of attacks are limited due to the constraint of the attack energy. First, this work proposes an attack model which implements two types of attacks cooperatively. Then, under the proposed attack model, the attack performance is quantified by deriving the error covariance matrix, which is more intricate than the existing results since it involves more related terms that include the decision variables of the multiple attacks. Based on this, the attack design problem is converted into an optimisation problem with more constraints and decision variables. By analyzing the structure of the error covariance, it is proved that solving the optimisation problem is equivalent to step-wisely resolving the optimal distribution of FDI attacks and the optimal scheduling of multiple attacks without losing optimality. And then, the optimal distribution is obtained by utilising the Lagrange multiplier method, and the optimal scheduling is solved by 0-1 programming, such that the optimal attack strategy is obtained. Finally, the results are validated through the simulation examples.

Date: 2026
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DOI: 10.1080/00207721.2025.2504646

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