Pinning Controllability for a Boolean Network With Arbitrary Disturbance Inputs

In this paper, pinning controllability for a Boolean network (BN) under arbitrary disturbance inputs is considered. By selecting a fraction of nodes as the pinning nodes and injecting controllers that depend on the values of the disturbance inputs of the previous time instant, the controllability can be guaranteed for any BNs under arbitrary disturbance inputs. First, based on the necessary and sufficient conditions for the controllability of a BN with arbitrary disturbance inputs obtained in this paper, a constructive method for designing the transition matrix of the BN is presented, which further provides a method for selecting the pinning nodes. Second, a logical relationship between the control input nodes and system nodes is provided through solving logical matrix equations. Third, the control input sequence algorithm is also given. Finally, an example is presented to show the effectiveness of the proposed results.