Firing Sequences Estimation in Vector Space Over $Z_{3}$ for Ordinary Petri Nets

Event sequences estimation is an important issue for fault diagnosis of Discrete event systems, so far as fault events cannot directly be measured. This paper is about event sequences estimation with Petri net models. Events are assumed to be represented with transitions, and firing sequences are estimated from measurements of the marking variation. Estimation with and without measurement errors are discussed in n-dimensional vector space over alphabet Z ₃ = {-1, 0, 1}. Sufficient conditions and estimation algorithms are provided. Performance is evaluated, and the efficiency of the approach is illustrated on two examples from manufacturing engineering.