On Active Learning for Supervisor Synthesis

Supervisory control theory provides an approach to synthesize supervisors for cyber-physical systems using a model of the uncontrolled plant and its specifications. These supervisors can help guarantee the correctness of the closed-loop controlled system. However, access to plant models is a bottleneck for many industries, as manually developing these models is an error-prone and time-consuming process. An approach to obtaining a supervisor in the absence of plant models would help industrial adoption of supervisory control techniques. This paper presents <tex-math notation="LaTeX">SupL* </tex-math> , an algorithm to learn a maximally permissive controllable supervisor in the absence of plant models. It does so by actively interacting with a simulation of the plant by means of queries. If the obtained supervisor is blocking, existing synthesis techniques are employed to prune the blocking supervisor and obtain the maximally permissive controllable and non-blocking supervisor. Additionally, this paper presents an approach to interface the <tex-math notation="LaTeX">SupL* </tex-math> with a PLC to learn supervisors in a virtual commissioning setting. This approach is demonstrated by learning a supervisor of the well-known Machine Buffer Machine example simulated in Xcelgo Experior and controlled using a PLC. <tex-math notation="LaTeX">SupL* </tex-math> interacts with the PLC and learns a maximally permissive controllable supervisor for the simulated system. Note to Practitioners—Ensuring the correctness of automated systems is crucial. Supervisory control theory proposes techniques to help build control solutions that have certain correctness guarantees. These techniques rely on a model of the system. However, such models are typically unavailable and hard to create. Active learning is a promising technique to learn models by interacting with the system to be learned. This paper aims to integrate active learning and supervisory control such that the manual step of creating models is no longer needed, thus, allowing the use of supervisory control techniques in the absence of models. The proposed approach is implemented in a tool and demonstrated using a case study.