Delay parameter identification for time-delay Boolean networks and Boolean control networks

This brief analyzes identification problems on delay parameter of time-delay Boolean networks (TBNs) and Boolean control networks (TBCNs). Using Cheng product, the algebraic forms of TBNs and TBCNs are obtained. On basis of the admissible output sequence, definitions on identifiability of delay parameter for TBNs and TBCNs are given. A result shows that a TBCN with state feedback control can be transformed into a TBN. And the TBN and the TBCN with networked control both can be converted into a set of subnetworks without time-delay in states. Then using the established output parameter matrices, the number of output sequences of each subnetwork can be calculated. Based on the relationship between a TBN (TBCN with networked control) and its subnetworks, the corresponding criterion is proposed to determine the delay parameter of the original system. Finally, an example is presented to demonstrate the effectiveness of the obtained results.