基于可达空间的结构化聚合马尔可夫模型约简

IF 7 1区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

IEEE Transactions on Automatic Control Pub Date : 2024-12-26 DOI:10.1109/TAC.2024.3523261

Man Zheng;Yoshito Ohta

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引用次数: 0

摘要

聚合马尔可夫模型（AMM）的阶数是复杂度的一个指标，与模型的可达子空间密切相关。当可达子空间不是整个空间时，称为可达空间可约。先前的结果表明，存在一种可能不满足非负约束的降阶拟实现，等价于给定的可达空间可约AMM。本文主要研究的是结构化的人工智能模型，其中转换矩阵和观测矩阵具有一定的结构化模式。给出了结构矩阵可达-空间可约的充分条件。此外，在这种情况下，我们证明了通过为可达空间的超集选择合适的基来获得实降阶实现，而不是准实现。最后，给出了实例来支持我们的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Reduction for Structured Aggregated Markov Models Based on Reachable Space

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.

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来源期刊

IEEE Transactions on Automatic Control 工程技术-工程：电子与电气

CiteScore

11.30

自引率

5.90%

发文量

824

审稿时长

9 months

期刊介绍： In the IEEE Transactions on Automatic Control, the IEEE Control Systems Society publishes high-quality papers on the theory, design, and applications of control engineering. Two types of contributions are regularly considered: 1) Papers: Presentation of significant research, development, or application of control concepts. 2) Technical Notes and Correspondence: Brief technical notes, comments on published areas or established control topics, corrections to papers and notes published in the Transactions. In addition, special papers (tutorials, surveys, and perspectives on the theory and applications of control systems topics) are solicited.