A New Approach for Verification of Delay Coobservability of Discrete-Event Systems

TL;DR

This paper introduces an efficient polynomial-time method to verify delay coobservability in decentralized discrete-event systems, improving computational complexity over existing approaches.

Contribution

It proposes a novel verification approach for delay coobservability using language partitioning and verifier construction, with lower complexity than prior methods.

Findings

Verification complexity is polynomial in system size and delays.

The approach is more computationally efficient than existing methods.

Delay coobservability relates to delay K-codiagnosability, enabling cross-application of techniques.

Abstract

In decentralized networked supervisory control of discrete-event systems (DESs), the local supervisors observe event occurrences subject to observation delays to make correct control decisions. Delay coobservability describes whether these local supervisors can make sufficient observations. In this paper, we provide an efficient way to verify delay coobservability. For each controllable event, we partition the specification language into a finite number of sets such that strings in different sets have different lengths. For each of the sets, we construct a verifier to check if delay coobservability holds for the controllable event. The computational complexity of the proposed approach is polynomial with respect to the number of states, the number of events, and the upper bounds on observation delays and only exponential with respect to the number of local supervisors. It has lower complexity order than the existing approaches. In addition, we investigate the relationship between the decentralized supervisory control of networked DESs and the decentralized fault diagnosis of networked DESs and show that delay $K$-codiagnosability is transformable to delay coobservability. Thus, techniques for the verification of delay coobservability can be leveraged to verify delay $K$-codiagnosability.