Identification of Boolean control networks with time delay.

This paper investigates the identification of time-delay Boolean networks (TBNs) and time-delay Boolean control networks (TBCNs) via Cheng product. According to all admissible (input-)output sequences, definition on identifiability of the (TBCN) TBN is given. Two algorithms are designed to select suitable delay parameters of the TBN and TBCN, respectively. Based on these, the original systems are divided into several subsystems. Then by virtue of observability, the criteria for identifiability of the TBN and TBCN are obtained. Moreover, the corresponding constructing processes are presented to establish the internal structures of the TBN and TBCN. Finally, two illustrative examples are given to show the feasibility of the proposed methods.