Supervisory Control of Discrete Event Systems for Small Language Under Cyber Attacks

TL;DR

This paper addresses supervisory control in networked discrete event systems under cyber attacks, focusing on ensuring system behavior within a small language bound despite nondeterminism caused by cyber threats.

Contribution

It introduces CA-S-controllability and CA-S-observability, providing necessary and sufficient conditions for supervisory control under cyber attack conditions.

Findings

Supervisory control problem is solvable if the language is CA-S-controllable and CA-S-observable.

Conditions for the existence of infimal CA-S-controllable and CA-S-observable superlanguages.

Framework for designing supervisors under cyber attack-induced nondeterminism.

Abstract

Cyber attacks are unavoidable in networked discrete event systems where the plant and the supervisor communicate with each other via networks. Because of the nondeterminism in observation and control caused by cyber attacks, the language generated by the supervised system becomes nondeterministic. The small language is defined as the lower bound on all possible languages that can be generated by the supervised system, which is needed for a supervised system to perform some required tasks under cyber attacks. In this paper, we investigate supervisory control for the small language. After introducing CA-S-controllability and CA-S-observability, we prove that the supervisory control problem of achieving a required small language is solvable if and only if the given language is CA-Scontrollable and CA-S-observable. If the given language is not CA-S controllable and/or CA-S-observable, we derive conditions under which the infimal CA-S-controllable and CA-S-observable superlanguage exists and can be used to design a supervisor satisfying the given requirement.