Supervisory controller synthesis and implementation for safety PLCs

The development of supervisory controllers for cyber-physical systems is a laborious and error-prone process. Supervisor synthesis enables control designers to automatically synthesize a correct-by-construction supervisor from a model of the plant combined with a model of the control requirements. From the supervisor model, controller code can be generated which is suitable for the implementation on a programmable logic controller (PLC). Supervisors for industrial systems that operate in close proximity to humans have to adhere to strict safety standards. To achieve these standards, safety PLCs (SPLCs) are used. For SPLC implementation, the supervisor has to be split into a regular part and a safety part. In previous work, a method is proposed to automatically split a supervisor model for this purpose. The method assumes that the provided plant model is a collection of finite automata. In this paper, the extension to extended finite automata is described. Additionally, guidelines are provided for modeling the plant and the requirements to achieve a favorable splitting. A case study on a rotating bridge is elaborated which has been used to validate the method. The case study spans all development steps, including the implementation of the resulting supervisor to control the real bridge.

Hierarchical planning in a supervisory control context with compositional abstraction

Hierarchy is a tool that has been applied to improve the scalability of solving planning problems modeled using Supervisory Control Theory. In the work of Hill and Lafortune (2016), the notion of cost equivalence was employed to generate an abstraction of the supervisor that, with additional conditions, guarantees that an optimal plan generated on the abstraction is also optimal when applied to the full supervisor. Their work is able to improve their abstraction by artificially giving transitions zero cost based on the sequentially-dependent ordering of events. Here, we relax the requirement on a specific ordering of the dependent events, while maintaining the optimal relationship between upper and lower levels of the hierarchy. This present paper also extends the authors’ work (Vilela and Hill 2020) where we developed a new notion of equivalence based on cost equivalence and weak bisimulation that we term priced-observation equivalence. This equivalence allows the supervisor abstraction to be generated compositionally. This helps to avoid the explosion of the state space that arises from having to first synthesize the full supervisor before the abstraction can be applied. Here, we also show that models with artificial zero-cost transitions can be created compositionally employing the new relaxed sequential dependence definition. An example cooperative robot control application is used to demonstrate the improvements achieved by the compositional approach to abstraction proposed by this paper.