Observer Design for Timed Automata under No Observation

This paper considers a class of timed discrete event systems (DESs) with a single clock. The timing structure is characterized by a timing function and a clock resetting function, where the former restricts transitions to occur when the clock takes a value in a given time interval, and the latter indicates how the clock value is updated upon the occurrence of transitions. Given a set of current discrete states in which the system can be, we assume that no information on the occurrence of events is captured (all such information is destroyed or lost), and only the clock that measures the time is reliable. We propose a state observer, in terms of a deterministic finite automaton, which enables us to compute the set of states in which the system can be at a certain time instant. The proposed observer is the basic step towards the construction of an observer that considers both unobservable and observable evolutions. Thus it can be considered as a first step in solving various problems related to partial observation of timed DESs such as opacity Verification, fault diagnosis and diagnosability analysis.