Predictability for Finite State Machines: a set-membership approach

Approximate predictability of Pseudo-Metric Systems

“…Approximate predictability corresponds to the possibility of distinguishing, on the basis of the observations collected in a certain time interval [t 0 ; T ] and in at most Δ > 0 time steps (i.e., within T + Δ), state runs that will reach for the first time the set of faulty states F from both state runs that will not reach the set B ρ (F) and state runs that already reached F at a previous time instant t < T. The definition above extends to pseudo-metric systems the notion of (exact) predictability given in [2], see also [3,10], for FSMs. In particular, when ρ = 0, the definition above coincides with the one given in [2]. Checking approximate predictability of symbolic pseudo-metric systems is a decidable problem with polynomial computational complexity.…”

“…[4]. In this contribution we introduce the notion of approximate predictability which extends to the general class of pseudo-metric systems, the notion of (exact) predictability given in [2], see also [3,10], for finite state machines. Pseudo-metric systems are a powerful modeling framework to deal with complex heterogeneous systems such as hybrid systems.…”

Critical Observability for Automata and Petri Nets

“…The state estimation problem is one of the central problems in cyber-physical systems that is of importance, e.g., in safetycritical applications where we need to estimate the current state of a system in the case we have an incomplete information of its behavior. Eminent examples of the state estimation problem are, for example, fault diagnosability [9], [41], [42] asking whether a fault event has occurred and whether its occurrence can be detected within a finite delay, opacity [3], [4], [17], [20], [26], [35], [37], a property related to the privacy and security analysis, asking whether the system reveals its secret to a passive observer (an intruder), detectability [28], [29], [43] asking whether the current and subsequent states can be determined based on observations, marking observability [14] concerning the estimation of the marking of a Petri net, and predictability [12], [13] concerning the future occurrence of a state or of an event.…”