Verification of Detectability for Unambiguous Weighted Automata

• 成果类型: Article
• 署名作者: Lai, Aiwen; Lahaye, Sebastien; Giua, Alessandro
• 署名单位: Universite d'Angers; University of Cagliari
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2995173
• 发表日期: 2021
• 页码: 1437-1444
• 关键词: automata; observers; indexes; Discrete-event systems; Petri nets; Detectability; discrete event systems; State estimation; weighted automata (WA)

摘要

In this article, we deal with the detectability problem for unambiguous weighted automata (UWAs). The problem is to determine if, after a finite number of observations, the set of possible states is reduced to a singleton. Four types of detectabilities, namely, strong detectability, detectability, strong periodic detectability, and periodic detectability are defined in terms of different requirements for current state estimation. We first construct a deterministic finite state automaton (called observer) over a weighted alphabet and prove that it can be used as the current-state estimator of the studied UWA. Finally, necessary and sufficient conditions based on the observer are proposed to verify detectabilities of a UWA.