Detectability of discrete event systems with dynamic event observation

Our previous work considered detectability of discrete event systems which is to determine the current state and subsequent states of a system based on the event observation. We assume that the event observation is static, that is, if an event is observable, then all its occurrences are observable. This requires that all sensors be turned on all the time. However, in practical systems such as sensor networks, in order to reduce cost or save energy, the event observation often needs to be dynamic, that is, the occurrences of the same events may or may not be observable, depending on the state of the system. In this paper, we generalize static event observation into dynamic event observation and consider the detectability problem under the dynamic event observation. As before, we define four types of detectabilities. To check detectabilities, we construct the observer with exponential complexity. We can also construct a detector with polynomial complexity to check strong detectabilities. Dynamic event observation can be implemented in two possible ways: a passive observation and an active observation. For the active observation, we discuss how to find minimal event observation policies that preserve four types of detectabilities respectively.