Towards a UTP Semantics for Modelica

Abstract

Abstract. We describe our work on a UTP semantics for the dynamic systems modelling language Modelica. This is a language for modelling a system's continuous behaviour using a combination of differentialalgebraic equations and an event-handling system. We develop a novel UTP theory of hybrid relations, inspired by Hybrid CSP and Duration Calculus, that is purely relational and provides uniform handling of continuous and discrete variables. This theory is mechanised in our Isabelle implementation of the UTP, Isabelle/UTP, with which we verify some algebraic properties. Finally, we show how a subset of Modelica models can be given semantics using our theory. When combined with the wealth of existing UTP theories for discrete system modelling, our work enables a sound approach to heterogeneous semantics for Cyber-Physical systems by leveraging the theory linking facilities of the UTP.

Behavioural Models for FMI Co-simulations

“…In particular, we are interested in hybrid models, involving FMUs defined by languages for discrete and for continuous modelling. To cater for models involving continuous FMUs, we plan to use a Circus extension [13]. Using current support for Circus in Isabelle [14], we may also be able to explore code generation from the models.…”

“…Circus can currently cater only for discrete-time models. On the other hand, a continuous time extension of Circus that can be used to give semantics to continuous-systems simulations [13] is under development.…”

Towards Semantically Integrated Models and Tools for Cyber-Physical Systems Design

“…CPSs are usually represented by hybrid computational models consisting of both discrete and continuous variables, and thus we first develop a UTP theory of hybrid relations [11]. In addition to discrete input and output variables this theory also provides support for continuous variable trajectories x : R → R. The healthiness condition for this theory is called HCT : it ensures that variables are piecewise continuous over a particular interval of time.…”

“…Finally the whole system iterates. We have used our hybrid relational calculus to give a semantics to a subset of Modelica, which elaborates the latter's event handling system [11]. Moreover we have mechanised the calculus in our Isabelle based theorem prover for UTP [12], which enables automated proof about hybrid relations.…”

Towards Verification of Cyber-Physical Systems with UTP and Isabelle/HOL

“…Hoare & He [24] show how the alphabetised relational calculus can be applied to construct a hierarchy of such theories, including simple imperative programs (relations), designs that correspond to preand postcondition specifications, and various theories of concurrent and parallel programs, including the process algebras ACP, CCS, and CSP [23]. Since the advent of UTP, a host of additional UTP theories have been developed that variously tackle paradigms like real-time programming [34], object-oriented programming [32], security and confidentiality [3], mobile processes [33], probabilistic modelling [6], and hybrid systems [15]. Moreover, the FMI API itself has been given a UTP-based semantics [9] that can be used as an interface to the semantic model of individual FMUs, and also allows a network of FMUs to be verified at this level using the FDR3 refinement checker [18].…”