On Optimal Time-Varying Feedback Controllability for Probabilistic Boolean Control Networks

• Published in: IEEE transaction on neural networks and learning systems Vol. 31; no. 6; pp. 2202 - 2208
• Main Authors: Toyoda, Mitsuru, Wu, Yuhu
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.06.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive control; Algorithms; Boolean; Boolean algebra; Boolean functions; Computer simulation; Control systems; Control theory; Controllability; Feedback; Feedback control; Optimal control; Optimization; probabilistic Boolean control network (PBCN); Probabilistic logic; semitensor product (STP); Stability; State feedback; Statistical analysis; stochastic optimal control
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2019.2927241

This brief studies controllability for probabilistic Boolean control network (PBCN) with time-varying feedback control laws. The concept of feedback controllability with an arbitrary probability for PBCNs is formulated first, and a control problem to maximize the probability of time-varying feedback controllability is investigated afterward. By introducing semitensor product (STP) technique, an equivalent multistage decision problem is deduced, and then a novel optimization algorithm is proposed to obtain the maximum probability of controllability and the corresponding optimal feedback law simultaneously. The advantages of the time-varying optimal controller obtained by the proposed algorithm, compared to the time-invariant one, are illustrated by numerical simulations.