Reduction for Structured Aggregated Markov Models Based on Reachable Space

• 成果类型: Article
• 署名作者: Zheng, Man; Ohta, Yoshito
• 署名单位: Anhui University; Kyoto University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3523261
• 发表日期: 2025
• 页码: 3502-3509
• 关键词: hidden Markov models; vectors; Stochastic processes; SYMBOLS; Null space; Matrix decomposition; computational modeling; Tensors; Numerical models; POLYNOMIALS; Aggregated Markov models (AMM); Markov processes; reduced order modeling; state reduction; Stochastic systems

摘要

The order of an aggregated Markov model (AMM) is an index of complexity and is closely related to the reachable subspace of a model. The AMM is called reachable-space reducible when the reachable subspace is not the whole space. Previous results demonstrate that there exists a reduced-order quasi-realization, which may not satisfy the nonnegative constraints, equivalent to a given reachable-space reducible AMM. This article focuses on the structured AMM where the transition and observation matrices have certain structured patterns. Sufficient conditions are derived for a structured AMM to be reachable-space reducible. Moreover, in this case, we show that a real reduced-order realization, instead of a quasi-realization, is obtained by choosing suitable bases for supersets of the reachable space. Finally, examples are given to support our results.