Active prognosis and diagnosis of modular discrete-event systems

TL;DR

This paper develops methods for verifying and enforcing prognosability and diagnosability in modular discrete-event systems using automata theory, ensuring global properties through local supervisors.

Contribution

It introduces a novel approach to compute modular supervisors that enforce prognosability and diagnosability in complex systems, extending existing theory to modular DESs.

Findings

Algorithms for computing supremal prognosable and diagnosable sublanguages.

Demonstration of global properties achieved through local supervisors.

Examples illustrating the effectiveness of the proposed method.

Abstract

This paper addresses the verification and enforcement of prognosability and diagnosability for discreteevent systems (DESs) modeled by deterministic finite automata. We establish the equivalence between prognosability (respectively, diagnosability) and pre-normality over a subset of the non-faulty language (respectively, a suffix of the faulty language). We then demonstrate the existence of supremal prognosable (respectively, diagnosable) and normal sublanguages. Furthermore, an algorithm is then designed to compute the supremal controllable, normal, and prognosable (respectively, diagnosable) sublanguages. Since DESs are typically composed of multiple components operating in parallel, pure local supervisors are generally insufficient, as prognosability and diagnosability are global properties of a system. Given the limited work on enforcing prognosability or diagnosability in modular DESs, where these properties are enforced through local supervisors, this paper leverages a refined version of pre-normality to compute modular supervisors for local subsystems. The resulting closed-loop system is shown to be globally controllable, normal, and prognosable/ diagnosable. Examples are provided to illustrate the proposed method.