Controllability of generalized asynchronous Boolean networks with periodical impulsive control

The objective of this paper is to investigate the controllability of generalized asynchronous Boolean networks under periodical impulsive control. In order to attain the objective, the semi-tensor product is employed to transform generalized asynchronous Boolean networks that have periodic impulsive control into linear representations. The conversion provides the basis for deriving the general formula of the network transition matrix's dependence on the controller. Then three different control modes are used to define the controllability of generalized asynchronous Boolean networks: free Boolean sequence periodic impulsive control, input networked periodic impulsive control and feedback networked periodic impulsive control. For each mode, reachable sets of time s under a specific set of controls and arbitrary control are provided. The likelihood of transitioning from one state to another is also calculable. Finally, instances are given for a variety of control modes to illustrate the theorems' effectiveness and robustness.