We revisit the central notion of controllability in supervisory control theory from process-theoretic perspective. To this end, we investigate partial bisimulation preorder, a behavioral preorder that is coarser than bisimulation equivalence and finer than simulation preorder. It is parameterized by a subset of the set of actions that need to be bisimulated, whereas the actions outside this set need only to be simulated. This preorder proves a viable means to define controllability in a nondeterministic setting as a refinement relation on processes. The new approach provides for a generalized characterization of controllability of nondeterministic discrete-event systems. We characterize the existence of a deterministic supervisor and compare our approach to existing ones in the literature. It helped identify the coarsest minimization procedure for nondeterministic plants that respects controllability. At the end, we define the notion of a maximally permissive supervisor, nonblocking property, and partial observability in our setting.
|Title of host publication||Proceedings of the 2011 American Control Conference (ACC 2011, San Francisco CA, USA, June 29-July 1, 2011)|
|Place of Publication||Piscataway|
|Publisher||Institute of Electrical and Electronics Engineers|
|Publication status||Published - 2011|
Baeten, J. C. M., Beek, van, D. A., Luttik, S. P., Markovski, J., & Rooda, J. E. (2011). A process-theoretic approach to supervisory control theory. In Proceedings of the 2011 American Control Conference (ACC 2011, San Francisco CA, USA, June 29-July 1, 2011) (pp. 4496-4501). Institute of Electrical and Electronics Engineers.