Bridging discrete and continuous time models with atoms

Abstract

Recent trends in replacing traditionally digital components with analog counterparts in order to overcome physical limitations have led to an increasing need for rigorous modeling and simulation of hybrid systems. Combining the two domains under the same set of semantics is not straightforward and often leads to chaotic and non-deterministic behavior due to the lack of a common understanding of aspects concerning time. We propose an algebra of primitive interactions between continuous and discrete aspects of systems which enables their description within two orthogonal layers of computation. We show its benefits from the perspective of modeling and simulation, through the example of an RC oscillator modeled in a formal framework implementing this algebra.

ForSyDe-Atom

“…(1) We present the first comprehensive overview of the ForSyDe-Atom framework for modeling CPS, clarifying the main modeling concepts: layers, atoms, and patterns (introduced in Reference [46]), and introducing a new concept that enables systematic design flow: projection. 2We detail these modeling concepts by defining four separate layers capturing different aspects of CPS modeling: timing (introduced in References [45,46]), structured parallelism (introduced in References [46,48]), uncertainty, and component properties. 3We demonstrate the modeling framework through a formal, high-level, executable model of an AESA radar system composed of the signal processing chain (introduced in Reference [48]) alongside the radar environment dynamics.…”

“…In engineering practices rather than talking about causality, continuous systems are described by their dynamics, i.e., how the system evolves over time. In Reference [45], we presented a means to represent continua by virtue of abstraction, and in Reference [16] we discuss a detailed algebraic approach to the continuous time (CT) MoC. As such CT signals are not being sampled and approximated but rather represented as pure functions from the start.…”