Supervisory Control of Labeled Transition Systems Subject to Multiple Reachability Requirements via Symbolic Model Checking

Abstract

We present an algorithm to compute the unique maximally permissive state-based supervisor for any deterministic finite labeled transition system subject to a specification with combined invariance and reachability requirements. The specifications that we consider are expressed in computation tree logic and include specifications with multiple reachability requirements, each of which should always be satisfied. The form of the controller (a state-based supervisor) is purely memoryless, so the control decisions can be made by directly sampling the state of the system that is being controlled, without recording any past event or transition history. The algorithm has been implemented in SynthSMV, an extension of the well-known model-checking solver NuSMV, which uses NuSMV's efficient implementation of symbolic model checking (based on binary decision diagrams). A case study that involves coordinating the operation of a set of reactors in a chemical plant shows how the methods that we develop apply in practice.