Critical Observability of Stochastic Discrete Event Systems Under Intermittent Loss of Observations

A system is said to be critically observable if the operator can always determine whether the current state belongs to a set of critical states. Due to the communication failures, systems may suffer from intermittent loss of observations, which makes the system not critically observable. In this sense, to characterize critical observability in a quantitative way, this paper extends the notion of critical observability to stochastic discrete event systems modeled as partially observable probabilistic finite automata. Two new notions, called step-based almost critical observability and almost critical observability are proposed, which describe a measure of critical observability for a given system against intermittent loss of observations. We introduce a new language operation to obtain a probabilistic finite automaton describing the behavior of the plant system under intermittent loss of observations. Based on this structure, we also present verification methodologies to check the aforementioned two notions and analyze the complexity. Finally, the results are applied to a raw coal processing system, which shows the effectiveness of the proposed methods.