Sampled-data general partial synchronization of Boolean control networks

Abstract

In this manuscript, the general partial synchronization of a type of drive-response Boolean control networks (BCNs) is proposed for the first time and is addressed by sampled-data feedback control (SDFC). Different from all previous synchronization in the field of BCNs, the general partial generalization requires that the total number of the synchronized nodes exactly maintains at a pre-special value after finite-time step, and it removes the requirement on the anticipated synchronized nodes. To begin with, we define the general partial synchronization of derive-response BCNs based on the Hamming distance of two Boolean vectors. Subsequently, by utilizing the semi-tensor product (STP) of matrices, we obtain a series of criteria for BCNs to achieve general partial synchronization by SDFC. Then, the corresponding SDFC strategy is designed, under which the considered BCNs achieve general partial synchronization. Finally, these results are demonstrated by an illustrative numerical example.