A probabilistic Boolean network based on semi-Markov decision processes

An optimal control problem in a PBN with the help of the theory of Semi-Markov decision processes is studied. Specifically, a control model for a PBN as a first passage model for semi-Markov decision processes is firstly formulated and then an optimal control problem is solved for choosing optimal control inputs in a PBN such that an objective function related to system behavior is minimal. In order to illustrate the validity of our approach, an example is also displayed.