Interval-Based Simulation of Zélus IVPs using DynIbex

Abstract

Modeling continuous-time dynamical systems is a complex task. Fortunately some dedicated programming languages exist to ease this work. Zélus is one such language that generates a simulation executable which can be used to study the behavior of the modeled system. However, such simulations cannot handle uncertainties on some parameters of the system. This makes it necessary to run multiple simulations to check that the system fulfills particular requirements (safety for instance) for all the values in the uncertainty ranges. Interval-based guaranteed integration methods provide a solution to this problem. The DynIbex library provides such methods but it requires a manual encoding of the system in a general purpose programming language (C++). This article presents an extension of the Zélus compiler to generate interval-based guaranteed simulations of IVPs using DynIbex. This extension is conservative since it does not break the existing compilation workflow.