A graph formulation of some supervisory control problems

The paradigm of supervisory control can be applied to many discrete event systems. In the particular case of semi-Markov decision problems, control actions often consist of removing some controllable probability transitions to prevent the system from reaching sets of undesirable states. The choice of the transitions to be removed can be based on the minimization of a long range average cost criterion. The graph interpretation of the optimal supervisory control problem for a semi-Markov chain can then be formulated as a minimal cost cut problem