Aggregated Bisimulation and Identification of Finite-Valued Networks

• 成果类型: Article
• 署名作者: Ji, Zhengping; Zhang, Xiao; Cheng, Daizhan
• 署名单位: Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; Hong Kong Polytechnic University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3509334
• 发表日期: 2025
• 页码: 3346-3353
• 关键词: Probabilistic logic; vectors; trajectory; Heuristic algorithms; CONTROLLABILITY; computational modeling; Aerospace electronics; Upper bound; System identification; reduced order systems; aggregation; finite-valued networks; identification; semitensor product (STP) of matrices; simulation

摘要

We propose a method that combines aggregation and bisimulation to approximate large finite-valued networks by smaller models. With the algebraic state-space representation of a quotient system under observational equivalence, the aggregated bisimulation is performed by partitioning a network into blocks and replacing the dynamics of each block by that of its quotient system. If the aggregation is not a bisimulation, these quotient systems can be further replaced by probabilistic networks based on the relative frequency of transitions, which contain full information about the input-output dynamics. As an inverse problem of aggregation, simulated identification of finite-valued networks is studied. We give an upper bound on the minimal number of nodes required to identify a system, and design an online algorithm to reproduce the internal state dynamics from given input-output sequences. The results are illustrated with numerical examples.