An Optimization-Based Approach to Discover the Unobservable Behavior of a Discrete-Event System through Interpreted Petri Nets

This article deals with the problem of discovering a Petri net (PN) model of a discrete-event system, starting from the observation of long-event sequences. Precisely, given an interpreted PN (IPN) system modeling the relations between input and output events of the system (i.e., the reactive/observable behavior), the internal state evolutions of the system (i.e., the unobservable behavior) are first discovered and then modeled. The proposed unobservable discovery takes advantage of the novel concept of interpreted sequences, which better characterize the system and model the behavior by considering both observable markings (outputs) and transition firings (inputs). The unobservable modeling is approached as a net synthesis problem. It relies on an optimization-based procedure that identifies the complementary structure; in particular, places only are added to the original model. Note to Practitioners - Black-box identification procedures process an input-output sequence recorded for a long period of time during the functioning of a closed-loop controlled system, and then return a model of the system. However, even if these models simulate well the recorded sequence, they are not very accurate. Indeed, they simulate also other sequences that, in general, are not admitted by the real system. The method proposed here aims to make more accurate these models by discovering the unobservable behavior of a controlled system, related to evolutions of the internal state (and variables) of the system without changing the capability of simulating the observed behavior.