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This paper deals with the infinite-horizon optimal control problem forBoolean control networks (BCNs) with a discounted-cost criterion. This problemhas been investigated in existing studies with algorithms characterized by highcomputational complexity. We thus attempt to develop more efficient approachesfor this problem from a deterministic Markov decision process (DMDP)perspective. First, we show the eligibility of a DMDP to model the controlprocess of a BCN and the existence of an optimal solution. Next, two approachesare developed to handle the optimal control problem in a DMDP. One approachadopts the well-known value iteration algorithm, and the other resorts to theMadani's algorithm specifically designed for DMDPs. The latter approach canfind an exact optimal solution and outperform existing methods in terms of timeefficiency, while the former value iteration based approach usually obtains anear-optimal solution much faster than all others. The 9-state-4-input\textit{ara} operon network of the bacteria \textit{E. coli} is used to verifythe effectiveness and performance of our approaches. Results show that bothapproaches can reduce the running time dramatically by several orders ofmagnitude compared with existing work.

Optimal Control of Boolean Control Networks with Discounted Cost: An Efficient Approach based on Deterministic Markov Decision Process