Finite-time output tracking of probabilistic Boolean control networks

Abstract

This paper mainly concentrates on the issue of finite-time output tracking of probabilistic Boolean control networks (PBCNs). Two kinds of problems are considered: (1) the system tracks a fixed reference output signal (ROS); (2) the system tracks a time variant reference output trajectory (TVROT). For the first problem, we design an effective event-triggered controller to realize output tracking in probability one. An algorithm is offered to find the control invariant subset (CIS) of a set, and a triggering set sequence is constructed based on the CIS. Next, a necessary and sufficient condition is proposed to judge whether the system is trackable in probability one. For the second problem, a criterion is given to judge whether the initial state can generate TVROT with probability one and an algorithm is then provided to solve the corresponding control sequence. Furthermore, a profit function is established to solve the maximum tracking probability for the initial state which can not generate TVROT with probability one. Lastly, two examples are offered to explain the theoretical results.