Synthesizing Supervisors with a Minimum Control Base for Discrete-Event Systems

Controlling a discrete-event system commonly entails synthesizing a supervisor to ensure that the plant’s closed-loop behaviour respects a certain specification. In the traditional approach to this problem, if the desired behaviour is not controllable then the specification’s supremal controllable sublanguage is enforced instead. Here we invert the problem and formulate the Minimum Control Base Problem, with the goal of finding the minimum set of controllable events that guarantees controllability for the desired behaviour. We show that the sets of controllable events that maintain controllability for the desired behaviour form a complete lattice with respect to subset inclusion and that there is therefore a minimum capability supervisor for any desired sublanguage of the plant’s behaviour. We apply our techniques to the Small Factory problem and discuss further applications including systems design, dynamic discrete-event systems, and biological systems.