Proof-Based Approach to Hybrid Systems Development: Dynamic Logic and Event-B

Abstract

The design of hybrid systems controllers requires one to handle both discrete and continuous functionalities in a single development framework. In this paper, we propose the design and verification of such controllers using a correct-by-construction approach. We use proof-based formal methods to model and verify the required safety properties of the given controllers. Both Event-B with Rodin, and hybrid programs and dynamic differential logic with KeYmaera are experimented on a common case study related to the modelling of a car controller. Finally, we discuss the lessons learnt from these experiments and draw the first steps towards a generic method for modelling hybrid systems in Event-B.

Handling Refinement of Continuous Behaviors: A Proof Based Approach with Event-B

“…In [12], we presented a generic approach to hybrid system modeling. This approach is inspired by the work of R. Back on continuous action systems [26], Platzer in [9] and R. Banach in [10], where both continuous and discrete behaviors are integrated in a single model definition.…”

“…In the remaining part of this paper, we show that the approach we developed in [12], makes it possible to define a refinement relation to refine an abstract continuous model by another one. Such a refinement is formalized in Event-B.…”

“…Our approach relies on proof and refinement based formal methods. We have shown in [12], [13] that Event-B [14] and its Integrated Development Environment (IDE) Rodin [15] support the design and proof of hybrid systems without requiring any extension. We devised a generic model that has been successfully deployed, using refinement, on various case studies borrowed from the literature [16], [17].…”

“…Objective of the paper. However, our approach [12], [13] mainly focuses on the design, by refinement, of the software part i.e. the controller assuming the plant is well and thoroughly defined.…”

Online Testing of Dynamic Reconfigurations w.r.t. Adaptation Policies

“…Определим тестовые случаи как последовательности контролируемых событий, которые отправляются в тестируемую систему с некоторой периодичностью. В случае адаптивных систем, которые являются гибридными системами, где дискретное и непрерывное время смешиваются, может быть принят дискретизированный подход, подобный описанному в [15]. В этом случае события, используемые для стимулирования системы, посылаются с заданной периодичностью, символизируемой тактами, длительность которых параметризована.…”