Optimal Control of Probabilistic Boolean Network using Embedding Framework

This paper deals with the optimal control of probabilistic Boolean control network (PBCN) in the Markov decision process (MDP) framework that avoids exhaustive search over all inputs. The optimal control problem of PBCN is efficiently tackled if it can be restructured into an equivalent linearly-solvable MDP (LMDP) formulation through the technique of embedding. However, i) the embedded state costs could disagree with original state costs and may even assume negative values, ii) determining the closeness of optimum continuous action of LMDP with discrete actions of the MDP is non-trivial. We propose a novel technique to implement for exact embedding where the embedded state costs match that of the original system. In addition a maximum a posteriori probability based method is proposed to obtain optimum discrete input for PBCN. A couple of examples are presented to illustrate the functioning of the proposed approach.