Guaranteed Error Bounds on Approximate Model Abstractions Through Reachability Analysis

Luca Cardelli, Mirco Tribastone, Max Tschaikowski, Andrea Vandin

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Abstract

It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem for nonlinear ordinary differential equations (ODEs) with polynomial derivatives. We introduce approximate differential equivalence as a more permissive variant of a recently developed exact counterpart, allowing ODE variables to be related even when they are governed by nearby derivatives. We develop algorithms to (i) compute the largest approximate differential equivalence; (ii) construct an approximate quotient model from the original one via an appropriate parameter perturbation; and (iii) provide a formal certificate on the quality of the approximation as an error bound, computed as an over-approximation of the reachable set of the perturbed model. Finally, we apply approximate differential equivalences to study the effect of parametric tolerances in models of symmetric electric circuits.
Original languageEnglish
Title of host publicationQuantitative Evaluation of Systems
Volume11024
PublisherSpringer
Publication date2018
Pages104-121
ISBN (Print)978-3-319-99153-5
DOIs
Publication statusPublished - 2018
Event15th International Conference on Quantitative Evaluation of SysTems - Beijing, China
Duration: 4 Sep 20187 Sep 2018
Conference number: 15
http://www.qest.org/qest2018/

Conference

Conference15th International Conference on Quantitative Evaluation of SysTems
Number15
CountryChina
CityBeijing
Period04/09/201807/09/2018
Internet address
SeriesLecture Notes in Computer Science
Volume11024
ISSN0302-9743

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