Fault detection of Boolean control networks

In this paper we address the fault detection problem for Boolean control networks (BCNs), by resorting to the algebraic approach recently introduced by D. Cheng and co-authors. To this end, we first investigate the properties of the set of input/output trajectories of a BCN. Specifically, we introduce the concepts of completeness and T-completeness, borrowed from the behavior theory of J.C. Willems, and show that completeness is always guaranteed, while T-completeness is a nontrivial property. In particular, we show that the reconstructibility property of a BCN always ensures T-completeness, but the converse is not true. Based on these results, we introduce the simple set-up of a BCN that can be either faulty or non-faulty, we define the concept of meaningful fault, and investigate under what conditions a meaningful fault can be detected from the input/output trajectories of the BCN.