Combating Curse of Dimensionality in Resilient Monitoring Systems: Conditions for Lossless Decomposition

Resilient monitoring systems (RMSs) are sensor networks that degrade gracefully under cyber-attacks on their sensors. The recently developed RMSs, while being effective in the attacked sensors identification and isolation, exhibited a drawback in their operation-an exponentially increasing assessment time as a function of the number of sensors in the network. To combat this curse of dimensionality, a decomposition approach has been proposed, which led to a dramatic reduction of the assessment time, irrespective of the sensor network dimensionality. However, information losses and, thus, reductions in the level of resiliency due to the decomposition, have not been investigated. This paper is intended to carry out such an investigation. Specifically, it derives conditions for lossless decomposition in terms of the Renyi-2 entropy. The development is based on the analysis of matrices, which characterize coupling of process variables and on a monotonicity property of the Dempster-Shafer combination rule on a class of functions, which arise within the RMS operation.