No synthesis needed, we are alright already

Abstract

Supervisory control theory provides means to synthesize supervisors for cyber-physical systems based on models of the uncontrolled plant and models of the control requirements. In general, it has been shown that supervisory control synthesis is NP-hard, which is not beneficial for the applicability to industrial-sized systems. However, supervisory control synthesis seems to be easy for several industrial-sized systems compared to the theoretical worst-case complexity. In this paper, we propose properties to identify easy supervisory control problems. When a system satisfies these properties, we show that the plant models and the requirement models together are a controllable, nonblocking, and maximally permissive supervisor, i.e., no synthesis is needed to calculate a supervisor. Furthermore, these properties allow for local verification of each plant and requirement model separately.