A major objective for constructing gene regulatory networks is to use them as models for designing optimal
therapeutic intervention policies within the context of synchronous or asynchronous probabilistic Boolean networks
(PBNs). However, most of the previous works focused on the former and only few studied the latter. This paper deals with
an optimal control problem in a generalized asynchronous PBN by applying the theory of controlled semi-Markov
processes. Specifically, we first describe a control model for a generalized asynchronous PBN as a controlled semi-
Markov process model and then solve the corresponding optimal control problem such that the probability that the
network reaches a prescribed reward level during a first passage time to some target set is maximal. Numerical examples
are then given to demonstrate the effectiveness of the proposed methods.
Keywords: Controlled semi-Markov processes, gene regulatory networks, generalized asynchronous probabilistic Boolean
network, optimal control, optimal policy.
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