Petri net-based automated control synthesis for a class of DEDS

The automated control synthesis of a class of discrete-event dynamic systems (DEDS) is presented in this paper. The speciality of the class consists in the fact that DEDS can be described by the kind of Petri nets (PN) named bounded Petri nets (BPN). While the capacity of BPN places is finite, there are no restrictions on the BPN structure. Thus, BPN represent a rather wide class of PN. In this approach the reachability tree (RT) of the BPN-based model of DEDS is understood to be the ordinary directed graph (ODG). To find feasible trajectories from a given initial state x/sub 0/ to a prescribed terminal state x/sub t/ a special intersection of both the straight-lined reachability tree (SLRT) and the backtracking reachability tree (BTRT) is performed. While the SLRT is developed from x/sub 0/ towards x/sub t/ the BTRT is developed from the x/sub t/ towards x/sub 0/. However, paths of the BTRT are oriented towards x/sub t/. The transpose of the adjacency matrix of the ODG is utilized for computing the SLRT while the adjacency matrix itself is utilized in order to compute the BTRT. Two approaches based on bipartite directed graphs (BDG) are introduced too.