Controllability for Nondeterministic Discrete-Event Systems with Data

Abstract

Supervisory control ensures safe coordination of the discrete-event behavior of the components of a given system. Models of supervisory control software are automatically synthesized based on formal models of the unsupervised system and the coordination requirements. To provide for a greater modeling convenience and to better the expressivity of the model-based systems and software engineering framework, several extensions of supervisory control theory with variables have been proposed. Supervisory control theory studies automated synthesis of supervisory controllers, where the central notion of controllability characterizes the notion of a model of a supervisory controller. One of the most prominent extensions of the theory with data is implemented by means of extended finite automata with variables. We revisit the notion of controllability for these models and we show that the relations that capture existing notions of controllability for finite automata with variables do not have desirable algebraic properties, i.e., they are not a preorders. We propose an alternative notion of controllability based on a behavioral relation termed partial bisimulation. We show that the proposed extension of partial bisimulation for finite automata with variables subsumes existing notions and we discuss its role in a proposed model-based engineering framework.