Controllability and observability of Boolean control networks subject to stuck-at fault

Fault-tolerant control is a fundamental and challenging branch in the control community, and has wide applications in aerospace, automotive technology and nuclear engineering. Particularly, the study of faulty Boolean control networks (BCNs) is meaningful to the gene engineering. This paper focuses on the stuck-at fault occurring in BCNs, and investigates the controllability and observability of faulty BCNs. The basic mathematical tool is semi-tensor product (STP) of matrices, which is used to determine the algebraic formulation of BCNs subject to the meaningful stuck-at fault. Through the construction of faulty matrix, the relation between stuck-at fault and controllability of BCNs is presented. In addition, the observability of BCNs subject to stuck-at fault is discussed. Several new criteria are derived for the controllability and observability of BCNs subject to stuck-at fault, which have lower complexity than that of original BCNs. Finally, the obtained results are applied to analyze the controllability and observability of an faulty apoptosis network.