Supervisory Control of Discrete Event Systems Modeled by Mealy Automata with Nondeterministic Output Functions

Abstract

Supervisory control is a general framework of logical control of discrete event systems. A supervisor assigns a set of control-disabled controllable events based on observed events so that the controlled discrete event system generates specified languages.
In conventional supervisory control, it is assumed that observed events are determined by internal events deterministically. But, this assumption does not hold in a discrete event system with sensor errors and a mobile system, where each observed event depends on not only an internal event but also a state just before the occurrence of the internal event. In this paper, we model such a discrete event system by a Mealy automaton with a nondeterministic output function. We introduce two kinds of supervisors: one assigns each control action based on a permissive policy and the other based on an anti-permissive one. We show necessary and sufficient conditions for the existence of each supervisor. Moreover, we discuss the relationship between the supervisors in the case that the output function is determinisitic.