Policy Iteration Approach to the Infinite Horizon Average Optimal Control of Probabilistic Boolean Networks

• Published in: IEEE transaction on neural networks and learning systems Vol. 32; no. 7; pp. 2910 - 2924
• Main Authors: Wu, Yuhu, Guo, Yuqian, Toyoda, Mitsuru
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.07.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Arabinose operon; Biological system modeling; Boolean; Boolean algebra; Boolean functions; Boolean networks (BNs); Coils; Heuristic algorithms; infinite horizon problem; logical networks; Optimal control; Optimization; probabilistic BNs (PBNs); Probabilistic logic; semitensor product (STP) of matrix; Signal processing algorithms; State feedback
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2020.3008960

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.