State Reconstruction Under Malicious Sensor Attacks

This paper considers the state reconstruction problem for discrete-time cyber-physical systems when some of the sensors can be arbitrarily corrupted by malicious attacks where the attacked sensors belong to an unknown set. We first prove that the state is $s$-error correctable if the system under consideration is $s$-sparse observable where $s$ denotes the maximum number of attacked sensors. Then, two state reconstruction methods are presented where the first method is based on searching elements with the same value in a set and the second method is developed in terms of searching element satisfying a given condition. In addition, after establishing and analyzing the conditions that the proposed state reconstruction methods are not effective, we address that it is very hard to prevent the state reconstruction when either state reconstruction method proposed in this paper is used. The correctness and effectiveness of the proposed methods are examined via an example of four-dimensional dynamic systems and a real-world example of three-inertia systems.