Stepwise Development of Simulink Models Using the Refinement Calculus Framework

Abstract

Simulink is a popular tool for model-based development of control systems. However, due to the complexity caused by the increasing demand for sophisticated controllers, validation of Simulink models is becoming a more difficult task. To ensure correctness and reliability of large models, it is important to be able to reason about model parts and their interactions. This paper provides a definition of contracts and refinement using the action systems formalism. Contracts enable abstract specifications of model parts, while refinement offers a framework to reason about correctness of implementation of contracts, as well as composition of model parts. An example is provided to illustrate system development using contracts and refinement.

Refinement-based verification of sequential implementations of Stateflow charts

“…While this approach ends in a graphical notation, namely Petri nets, we take the opposite direction: from a graphical notation to a program. In [2], the refinement calculus is adapted to Simulink diagrams, but they do not cover Stateflow charts, and their goal is not the verification of implementations, but the development of diagrams from contracts. In [20], a semantics for µ-Charts is constructed in Z, and a notion of refinement of µ-Charts is derived from the existing Z refinement calculus.…”

Supporting Modularity in Simulink Models

“…The drawback is a loss of direct visibility of data flow, so we will not incorporate it in our work. The use of pre-/post-condition contracts as verifiable interface specifications for Subsystems has also been proposed [4,5,14]. While this design-by-contract approach provides a way of ensuring desired behaviour at the Subsystem-level, our approach aims to document the interface syntax in a complete fashion at the Model-level.…”

Adapting modeling environments to domain specific interactions

“…The approach in [71] only preserves behavioral regression on flat state machines. Furthermore, approaches based on µ-calculus, B, and as described in [23] require additional proofs or simulations. The remaining approaches do not integrate any such guaranties or analysis in the refinements.…”

“…[87]. Nevertheless, Boström et al [23] presented a refinement calculus for Simulink to provide additional capabilities for stepwise development, which is not included by default within Simulink. As with our approach, the purpose of the work from Boström et al is to make common development practices more predictable and usable.…”

“…There is a considerable amount of Statecharts refinement approaches proposed in the literature where the main concern is to preserve the behavior of the original model [104,110,54,119,23,100]. This is a necessary condition to refine a model.…”