A Supervisory Control Algorithm Based on Property-Directed Reachability

TL;DR

This paper introduces a novel controller synthesis algorithm for discrete event systems using property-directed reachability, aiming to produce safe, minimally restrictive supervisors with formal guarantees.

Contribution

It adapts the PDR model checking algorithm to the domain of supervisory control, providing a correct-by-design synthesis method for DES controllers.

Findings

Algorithm successfully synthesizes safe controllers with minimal restrictions.

Experimental results demonstrate the approach's potential in formal supervisory control.

The method integrates formal verification techniques into control synthesis workflows.

Abstract

We present an algorithm for synthesising a controller (supervisor) for a discrete event system (DES) based on the property-directed reachability (PDR) model checking algorithm. The discrete event systems framework is useful in both software, automation and manufacturing, as problems from those domains can be modelled as discrete supervisory control problems. As a formal framework, DES is also similar to domains for which the field of formal methods for computer science has developed techniques and tools. In this paper, we attempt to marry the two by adapting PDR to the problem of controller synthesis. The resulting algorithm takes as input a transition system with forbidden states and uncontrollable transitions, and synthesises a safe and minimally-restrictive controller, correct-by-design. We also present an implementation along with experimental results, showing that the algorithm has potential as a part of the solution to the greater effort of formal supervisory controller synthesis and verification.