Two-staged approach for estimation of sequences in partially observable P-time Petri nets on a sliding horizon with schedulability analysis

In this paper, we consider the on-line estimation of current subsequences for Partially Observable P-time Petri Nets and their starting markings on a sliding horizon composed of steps defined by two successive occurrences of observable transition firings. We propose a general strategy composed of two phases: Phase 1 exploits a simplification of the P-time Petri net under the form of a Timed Petri net; considering a candidate count vector and the relevant starting marking proposed at Phase 1, Phase 2 makes a schedulability analysis by building a system of relations which can be represented by an acyclic conflict-free computation graph. The complete approach avoids the generation of sets which is generally time and space consuming, and provides an optimal solution for each subproblem by using efficient standard tools.