Towards Mapping Control Theory and Software Engineering Properties using Specification Patterns

A traditional approach to realize self-adaptation in software engineering (SE) is by means of feedback loops. The goals of the system can be specified as formal properties that are verified against models of the system. On the other hand, control theory (CT) provides a well-established foundation for designing feedback loop systems and providing guarantees for essential properties, such as stability, settling time, and steady state error. Currently, it is an open question whether and how traditional SE approaches to self-adaptation consider properties from CT. Answering this question is challenging given the principle differences in representing properties in both fields. In this paper, we take a first step to answer this question. We follow a bottom up approach where we specify a control design (in Simulink) for a case inspired by Scuderia Ferrari (F1) and provide evidence for stability and safety. The design is then transferred into code (in C) that is further optimized. Next, we define properties that enable verifying whether the control properties still hold at code level. Then, we consolidate the solution by mapping the properties in both worlds using specification patterns as common language and we verify the correctness of this mapping. The mapping offers a reusable artifact to solve similar problems. Finally, we outline opportunities for future work, particularly to refine and extend the mapping and investigate how it can improve the engineering of self-adaptive systems for both SE and CT engineers.