Synchronous probabilistic Boolean networks (PBNs) and generalized asynchronous PBNs have received significant attention over the past decade as a tool for modeling complex genetic regulatory networks. From a biological perspective, the occurrence of interactions among genes, such as transcription, translation, and degradation, may require a few milliseconds or even up to a few seconds. Such a time delay can be best characterized by generalized asynchronous PBNs. This paper attempts to study an optimal control problem in a generalized asynchronous PBN by employing the theory of average value-at-risk (AVaR) for finite horizon semi-Markov decision processes. Specifically, we first formulate a control model for a generalized asynchronous PBN as an AVaR model for finite horizon semi-Markov decision processes and then solve an optimal control problem for minimizing average value-at-risk criterion over a finite horizon. In order to illustrate the validity of our approach, a numerical example is also displayed.
Policy Iteration Approach to the Infinite Horizon Average Optimal Control of Probabilistic Boolean Networks