Model matching for finite-state machines

The problem of model matching for finite state machines (FSMs) consists of finding a controller for a given open-loop system so that the resulting clo sed-loop system matches a desired input-output behavior. In this paper, a s et of model matching problems is addressed: strong model matching (where th e reference model and the plant are deterministic FSMs and the initial cond itions are fixed), strong model matching with measurable disturbances (wher e disturbances are present in the plant), and strong model matching with no ndeterministic reference model (where any behavior out of those in the refe rence model has to be matched by the closed-loop system). Necessary and suf ficient conditions for the existence of controllers for all these problems are given. A characterization of all feasible control laws is derived and a n efficient synthesis procedure is proposed. Further, the well-known superv isory control problem for discrete-event dynamical systems (DEDSs) formulat ed in its basic form is shown to be solvable as a strong model matching pro blem with measurable disturbances and nondeterministic reference model.