A qualitative assessment of $$\alpha $$ α Rby in the perspective of the supervisory control theory

Abstract

It becomes more and more evident today that SAT-solving approaches have the potential to verify properties and synthesize supervisors of controlled systems described with a high level of abstraction. Such approaches can be particularly appropriate when engineers give more importance to decentralized, hierarchical, and parameterized control paradigms than to centralized ones in the design of systems composed of multiple small agents. One advantage of declarative programming languages, such as relational logic, in specifying control problems, including their underlying properties and reasoning methods, is their proximity to the mathematical objects used in the formulation of the theory itself, which allows for implementing new fragments of it faster. The disadvantage is, however, that SAT-solving approaches do not lend themselves to efficient calculations of auxiliary objects involved in some control problems, even if they can be described with the logic at hand. In some cases, the latter is not sufficiently powerful to express the entire solution logically. Such difficulties can be circumvented with $$\alpha {\textsc {Rby}}$$ , a fusion of Alloy and Ruby. Based on earlier experiments conducted with Alloy, this paper provides a qualitative assessment of $$\alpha {\textsc {Rby}}$$ and reports on the results of new experiments with two fragments of the supervisory control theory: state-based control and decentralized control.