Generalized detectability for discrete event systems

Abstract

In our previous work, we investigated detectability of discrete event systems, which is defined as the ability to determine the current and subsequent states of a system based on observation. For different applications, we defined four types of detectabilities: (weak) detectability, strong detectability, (weak) periodic detectability, and strong periodic detectability. In this paper, we extend our results in three aspects. (1) We extend detectability from deterministic systems to nondeterministic systems. Such a generalization is necessary because there are many systems that need to be modeled as nondeterministic discrete event systems. (2) We develop polynomial algorithms to check strong detectability. The previous algorithms are based on observer whose construction is of exponential complexity, while the new algorithms are based on a new automaton called detector. (3) We extend detectability to D-detectability. While detectability requires determining the exact state of a system, D-detectability relaxes this requirement by asking only to distinguish certain pairs of states. With these extensions, the theory on detectability of discrete event systems becomes more applicable in solving many practical problems.

Detectability of networked discrete event systems

“…Shu and Lin [19] and Shu et al [20] investigate state estimates and detectability systematically. Detectability is defined as the ability to determine the current state and subsequent states of a system based on observation.…”

“…Detectability is defined as the ability to determine the current state and subsequent states of a system based on observation. In [19], four types of detectabilities are defined with different uses in different applications. Intuitively, they can be explained as follows.…”

“…Instead, we may need to check whether the system stays in subset of states after finite numbers of observations. Therefore, D-detectability was introduced and investigated by Shu and Lin [19]. D-detectability reduces the need of checking the current and subsequent states to just distinguish certain pairs.…”

“…In [19], Shu and Lin modified the work proposed in [20], and they used a nondeterministic automaton instead of deterministic automaton. However, [19] presented some extra work; for example, the authors devolved a technique, which called detector, to check strong detectability and periodic strong detectability with the polynomial complexity instead of exponential complexity.…”

“…However, [19] presented some extra work; for example, the authors devolved a technique, which called detector, to check strong detectability and periodic strong detectability with the polynomial complexity instead of exponential complexity. Another contribution of [19] was introducing D-detectability, which relaxes the requirement of estimating the current of the system to just distinguishing certain pairs of state. this type of detectability is useful in the case where determining the current state and subsequent states is too restrictive.…”