When is the Secure State-Reconstruction Problem Hard?

Yanwen Mao, Aritra Mitra, Shreyas Sundaram, Paulo Tabuada

Abstract: This paper addresses the problem of reconstructing the state of a linear time-invariant system from malicious sensor measurements. The first result establishes that this problem is, in general, NP-hard. We then identify classes of subproblems that can be solved in polynomial time. When there are at most s malicious sensors, the problem can be solved in polynomial time when each eigenvalue is observable by at least 2s+1 sensors. When each eigenvalue has geometric multiplicity one, this condition is equivalent to the system being 2s-sparse observable. In contrast, the situation becomes more nuanced when each eigenvalue is not observable by at least 2s+1 sensors, as we describe in detail in the paper.