Data and model-based switching observer for cyber-physical systems against sparse sensor attacks

Qingjie Wang, Yining Qian and An-Yang Lu

International Journal of Systems Science, 2026, vol. 57, issue 1, 1-13

Abstract: This paper studied the problem of secure state estimation in cyber-physical systems subjected to sparse sensor attacks. Considering that the problem of secure state estimation under sparse attacks is inherently NP-hard, we designed a non-fixed sequence switching observer to estimate system states. First, a data and model-based switching law is designed to guide the observer. In the switching law, a deep learning-based predictor is trained to predict the probability of the channels being attacked, which helps quickly locate the attacked channels. The model-based analysis method is utilised to ensure the reliability of the proposed observer. Second, a set cover optimisation method is proposed to reduce the number of candidate combinations, thereby decreasing computational complexity and further improving the accuracy of the data-based method. Additionally, sufficient conditions for generating reliable state estimates are obtained. Finally, the validity of the proposed method is demonstrated by two simulations. It is shown that the data and model-based methods can quickly identify the attacked channels and obtain reliable state estimates.

Date: 2026
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DOI: 10.1080/00207721.2025.2486163

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