A Solution of DEDS Control Synthesis Problems

Abstract

A new view on the control synthesis of DEDS (discrete event dynamic systems) is presented in this paper. Petri nets (PN), frequently used for DEDS modelling, are understood here in a form of corresponding oriented graphs (OG) where the nodes of the OG are represented by the PN positions and the OG edges involve the PN transitions. The adjacency matrix of such a graph (or better said its transpose) is utilized in the DEDS control synthesis procedure. It is used for generating the numerical form of the state reachability tree in both the case of the straight-lined system development (from a given initial state to a prescribed terminal one) and that of the backtracking one (from the prescribed terminal state to the initial one). A suitable combination of both the straight-lined development of the OG-based model and the backtracking one is used in order to perform the DEDS control synthesis. Namely, the coincidence both of the reachability trees yields possible trajectories of the system development. Corresponding sequences of the control discrete events are found just by means of the OG adjacency matrix.