A layered formal framework for modeling of cyber-physical systems

Abstract

Designing cyber-physical systems is highly challenging due to its manifold interdependent aspects such as composition, timing, synchronization and behavior. Several formal models exist for description and analysis of these aspects, but they focus mainly on a single or only a few system properties. We propose a formal composable framework which tackles these concerns in isolation, while capturing interaction between them as a single layered model. This yields a holistic, fine-grained, hierarchical and structured view of a cyber-physical system. We demonstrate the various benefits for modeling, analysis and synthesis through a typical example.

Bridging discrete and continuous time models with atoms

“…We address the problems posed in the previous section from the perspective of the ForSyDe-Atom framework for modeling CPS [2] in order to describe analog and mixed signal systems. This framework is defined as a domain-specific language (DSL) embedded in the functional programming language Haskell, and is founded on three basic principles of modeling: 1) the separation of the manifold concerns in CPS as individual interacting layers; 2) the deconstruction of semantics of each layer to their core in form of primitive building blocks called atoms; 3) the reconstruction of functional modules by composing atoms in form of patterns.…”

“…Introduced in [2], ForSyDe-Atom defines processes like in (1) as functional mappings from signal(s) to signal(s), using the same reasoning as [6]- [9]. As such, the main data type defined by the MoC layer is the signal S described in (2) as a stream of events.…”

“…The ForSyDe-Atom framework currently defines four atoms in the MoC layer as process constructors similar to [8], [12]. Along with the tagged signal (2) these establish a minimal algebra of timed/causal interactions capable of describing a wide variety of CPS models [2]. Each MoC overloads these atoms with its specific (operational) semantics.…”

“…On account of its $ component defined in (8) the recurring % process is able to take the next state signal ns st (0) , phase-shift it with τ , and use it as base for the same prepending mechanism that created st (0) in order to create st (1) (15). st (2) (16) is similarly constructed by "delaying" ns st (1) and so on. We thus have a recursive definition for the infinite signal st which describes the dynamics of the circuit in Fig.…”

“…This paper presents the approach adopted by the ForSyDe-Atom framework for modeling CPS [2] and our discussion gravitates around the circuit shown in Fig. 3a.…”