Employing behavioral preorders to define controllability for nondeterministic discrete-event systems

We employ the behavioral preorder termed partial bisimulation to define controllability for nondeterministic discrete-event systems. The preorder induces a refinements relation between the models of the controlled and the original system, that captures a notion of controllability. We define a notion of a model of a deterministic supervisory controller and we compare our approach to existing ones in the literature. We show that the equivalence relation, induced by the partial bisimulation preorder, can be employed to minimize the model of the unsupervised system. We develop an efficient minimization algorithm, by characterizing the preorders as partition-relation pairs under stability conditions.