Abstract
This article studies the optimal control of probabilistic Boolean control networks (PBCNs) with the infinite horizon average cost criterion. By resorting to the semitensor product (STP) of matrices, a nested optimality equation for the optimal control problem of PBCNs is proposed. The Laurent series expression technique and the Jordan decomposition method derive a novel policy iteration-type algorithm, where finite iteration steps can provide the optimal state feedback law, which is presented. Finally, the intervention problem of the probabilistic Ara operon in E. coil, as a biological application, is solved to demonstrate the effectiveness and feasibility of the proposed theoretical approach and algorithms.
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