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

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 PN controller. 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.