Learning Probabilistic Logical Control Networks: From Data to Controllability and Observability

• 成果类型: Article
• 署名作者: Lin, Lin; Lam, James; Shi, Peng; Ng, Michael K.; Lam, Hak-Keung
• 署名单位: University of Hong Kong; University of Adelaide; Obuda University; Hong Kong Baptist University; University of London; King's College London
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3524241
• 发表日期: 2025
• 页码: 3889-3904
• 关键词: Observability; CONTROLLABILITY; Probabilistic logic; mathematical models; Matrix converters; dynamic programming; Biological system modeling; Q-learning; proteins; optimal control; observability; probabilistic logical networks (PLNs); reinforcement learning (RL); semitensor product (STP)

摘要

This article studies controllability and observability problems for a class of mixed-valued probabilistic logical control networks (PLCNs). First, PLCN is transformed into the algebraic state-space representation (ASSR)-form by resorting to the semitensor product method. Then, the formulas are presented to calculate the lower and upper bounds of the transition probability matrix, which further derive the controllability and observability criteria. Furthermore, the ASSR-form of a PLCN can be regarded as a Markov decision process. Using the latter framework, we prove the equivalence between the controllability probability and the optimal state-value function, which is an iteration equation. Besides, the parallel extension technique transforms the observability of PLCNs into the set stabilization of an augmented system. The correspondence between observability probability and optimal state-value function is also derived. Afterward, based on the state-value function, the algorithms via the Q-learning technique are exploited to estimate the controllability and observability probabilities along with obtaining the corresponding optimal control sequences. Finally, all the theoretical results are elaborated via a genetic regulatory p53-Mdm2 network.