Static control of boolean networks using semi-tensor product operation

In this paper, we investigate static control of Boolean networks described in the framework of semi-tensor product (STP) operation. The control objective is to determine control input nodes and their logical values so as to stabilize the considered Boolean network to a desired fixed point or cycle. Using topology of Boolean networks such as incidence matrix and hub nodes, a set of appropriate control input nodes is selected, and based on STP operations, we assign constant control inputs so that the controlled network can converge to a prescribed fixed point or cycle. To validate applicability of the proposed scheme, we conduct a numerical study on the problem of determining control input nodes for a Boolean network representing hierarchical differentiation of myeloid progenitors.