Search

Consider a set of vectors in Rn, partitioned into two classes: normal vectors and malicious vectors, for which the number of malicious vectors is bounded but their identities are unknown. The paper provides an efficient way for achieving a resilient convex combination, which is a convex combination of only normal vectors. Compared with existing approaches based on Tverberg points, the proposed method based on the intersection of convex hulls has lower computational complexity. Simulations suggest that the proposed method can be applied to achieve resilience of consensus-based distributed algorithms against Byzantine attacks based only on agents' locally available information. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the computational complexity of reconstructing the state of a linear system from sensor measurements that have been corrupted by an adversary. The first result establishes that the problem is, in general, NP-hard. We then introduce the notion of eigenvalue observability and show that the state can be reconstructed in polynomial time when each eigenvalue is observable by at least 2 s + 1 sensors and at most s sensors are corrupted by an adversary. However, there is a gap between eigenvalue observability and the possibility of reconstructing the state despite attacks — this gap has been characterized in the literature by the notion of sparse observability. To better understand this, we show that when the A matrix of the linear system has unitary geometric multiplicity, the gap disappears, i.e., eigenvalue observability coincides with sparse observability, and there exists a polynomial time algorithm to reconstruct the state provided the state can be reconstructed. [ABSTRACT FROM AUTHOR]