Identification of a class of singular Boolean control networks

System identification, recognized as an inverse control problem, is a significant aspect of modern control theory. This study focuses on addressing the identification problem related to a specific category of singular Boolean networks (SBNs) and singular Boolean control networks (SBCNs). The introduction of two novel concepts, namely the admissibility and solvability matrices, enables the establishment of conditions for determining the existence and uniqueness of solutions for SBNs and SBCNs. Then criteria are deduced to identify the number of dynamic equations. Based on observability, controllability and detectability, several conditions are presented to characterize identification. Among them, two crucial results show: When the solution to an SBN or SBCN is unique, the SBN is identifiable if and only if it is observable, and the SBCN is identifiable if and only if it is O1-observable, which is the most general type of observability. Besides, effective algorithms are devised to implement identification. Furthermore, the study delves into the normalization issue using the admissibility matrix, which provides a possibility to reduce the identified SBN or SBCN to a lower-order BN or BCN.