Switched Boolean Network Identification under Multiple Samples

This paper investigates the challenging task of identifying switched Boolean networks (SBNs) with unknown initial subnetworks, leveraging the semi-tensor product tool. The inherent complexity arising from the lack of knowledge regarding the initial subnetwork necessitates a rigorous approach to identification. Initially, the observability of SBNs is discussed using a matrix-based method, providing foundational insights for subsequent identification analysis. We find the accurate one-to-one correspondence between states and outputs by taking time into account. Building on this correspondence and the observability property, the identification of state and output evolution rules is systematically addressed, leading to the proposition of a necessary and sufficient condition for successful SBN identification. Subsequently, an efficient algorithm is developed to implement the proposed identification approach. Finally, the theoretical findings are validated through an illustrative example.