Deterministic and Nonblocking Supervisory Control of Discrete Event Systems under Cyber Attacks

Abstract

We investigate deterministic and nonblocking supervisory control of discrete event systems under cyber-attacks using the ALTER (Attack Language for Transition-basEd Replacement) model. While prior works consider supervisory control that achieves either the large (upper bound) language or small (lower bound) language separately, deterministic supervisory control achieves both large language and small language at the same time to ensure that the language generated by the supervised system is unique and deterministic. We introduce two new concepts of CA-D-controllability and CA-D-observability and prove that they are necessary and sufficient for the existence of a deterministic supervisor. For nonblocking supervisory control, the objective is to ensure that the supervised system can always reach marked states under any attack scenario. We prove that relative closure, CA-D-controllability, and CA-D-observability together are necessary and sufficient for the existence of a nonblocking supervisor. We further develop methods to verify CA-D-controllability and CA-D-observability. We also illustrate our results using a robotic system example.