Deriving real-time action systems controllers from multiscale system specifications

This paper develops a method for deriving controllers for real-time systems in which the components of the system operate at different time granularities. To this end, we incorporate the theory of time bands into action systems, which allows one to structure a system into multiple abstractions of time. The framework includes a logic that facilitates reasoning about different types of sampling errors and transient properties (i.e., properties that only hold for a brief amount of time), and we develop theorems for simplifying proofs of hardware/software interaction. We formalise true concurrency and define refinement for the parallel composition of action systems. Our method of derivation builds on the verify-while-develop paradigm, where the action system code is developed side-by-side with its proof