Ramadge–Wonham (1987) is the theory of supervisory control of discrete-event systems. A self-acting plant G produces events; the event set splits Σ = Σ_c ∪ Σ_u into controllable and uncontrollable events.
- The supervisor can only disable controllable events, never force the plant. Its power is veto, not command — it can prevent a
Σ_cevent from occurring but cannot cause any event, and cannot touchΣ_uat all. - Supremal controllable sublanguage
supC(K). Given a desired specification languageK, there is a unique, polynomial-time-computable maximal controllable-and-observable sublanguage — the least-restrictive supervisor that enforces the spec. This makes supervisor synthesis mechanical: declare the property, compute the minimal set of events to disable. - Partial observation. The supervisor generally sees only a projection of the event stream (a masked / natural-projection view). Any specification that depends on unobserved events is unenforceable; enlarging the observable event set
Σ_ostrictly enlarges what can be controlled.
Connects to modal/temporal logic via Hennessy–Milner and bisimulation-invariance, to epistemic knowledge-based programs (control may depend only on what the supervisor knows), and upstream to Ashby's regulation (ashby).