Formal verification of observers supervising a cyber-physical system implemented using IEC 61499

A rigorous check is a significant phase in the design process of control programs of safety-critical cyber-physical systems. Here, we consider such programs to be implemented using IEC 61499 standard for industrial automation. After the check is performed (for example, using formal verification), the engineer needs to ensure that even in unexpected situations, the system will not fail during the runtime, and for this online verification methods can be utilized. In this work, we consider attaching monitors implemented as basic function blocks to the interface of the controller, thus having a property being monitored represented in the form of a state machine. Now, monitors make the system safer only if their quality is also ensured. Since their complexity is far lower than the complexity of the controller, they can be model checked, however, in the case of IEC 61499 function blocks, open-loop model checking will produce spurious counterexamples as it will allow combinations that are not possible according to the IEC 61499 function blocks semantics (e.g., data transferred without firing the event). The current work addresses this issue and proposes a method for close-loop model checking of monitors, using the non-deterministic twin of a controller under supervision. We present our approach using the system of two orthogonal pneumatic cylinders.