Supervisory control based on minimal cuts and Petri net sub-controllers coordination

Abstract

This paper addresses the synthesis of Petri net (PN) controller for the forbidden state transition problem with a new utilisation of the theory of regions. Moreover, as any method of control synthesis based on a reachability graph, the theory of regions suffers from the combinatorial explosion problem. The proposed work minimises the number of equations in the linear system of theory of regions and therefore one can reduce the computation time. In this paper, two different approaches are proposed to select minimal cuts in the reachability graph in order to synthesise a PN controller. Thanks to a switch from one cut to another, one can activate and deactivate the corresponding PNcontroller. An application is implemented in a flexible manufacturing system to illustrate the present method. Finally, comparison with previous works with experimental results in obtaining a maximally permissive controller is presented.

Theory of Regions for Control Synthesis without Computing Reachability Graph

“…For convenience, the policy of this work is called R 1 , our prior work [23] is called R 3 and the related research of Ghaffari et al [8] is called G 2 . Table 13 lists the comparison results of the first case study with three approaches of supervisory control.…”

“…In fact, based on PN properties and mathematical theories, one can speed up the synthesis process of PN controller. Consequently, the criterion of computation time of PN controllers will be a key factor in the comparison of this work with the previous ones [8,23].…”

“…In our previous works [21][22][23][24][25], a new method of minimal cuts in RG is developed using the theory of regions. Through this approach, we have also minimized the computational cost of PN supervisor using the TR on specific areas of the graph and not on the whole RG.…”

“…For a given PN (Figure 1a) [23], we firstly generate the reachability graph ( Figure 1b). Next, one can analyze the RG to determine existing basic cycles, the legal markings and the forbidden ones (marking ∈ MI).…”

On Minimal Unique Induced Subgraph Queries

“…With the increasing of graph data, graphs have been of extensive concern and deeply studied. The management and mining of graph data can effectively solve the analysis and processing problems of topological data [7][8][9]. One of the most important tasks in graph management is how to effectively answer the various queries in graph databases.…”