Supervisory Control with Complete Observations

Supervisory control is control of a behavior or, equivalently, of a discrete-event system in this chapter modeled as an automaton. Supervisory control is exerted by specifying after each observation the set of enabled events. The automaton then chooses an event from the subset of enabled events, makes a transition and produces the observed event, after which the process repeats. The logical control objectives of supervisory control are legal behavior and required behavior. Legal behavior is a formal language which specifies what the automaton is safely allowed to do. The required behavior is a formal language which specifies what the system is required to do such as the completion of tasks. The main theorem is then that there exists a supervisory control such that the formal language of the controlled automaton equals the specification if and only if the specification is a controllable sublanguage. An algorithm to determine whether a specification is controllable is provided as well as an algorithm to compute the supervisor. If the specification is not controllable then there exists a supremal controllable sublanguage of the specification and a corresponding supervisory control.

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