Rigorous Continuous Evolution of Uncertain Systems

Luca Geretti, Sanja Zivanovic Gonzalez, Pieter Collins, Davide Bresolin, Tiziano Villa

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

Abstract

Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide several theoretical improvements to the algorithm, including its extension to piecewise constant and sinusoidal approximations of uncertain inputs, updates on the affine approximation bounds and a generalized formula for the analytical error. In addition, we implemented the methodology in Ariadne, a library for the verification of continuous and hybrid systems. Then we evaluated ten systems with varying degrees of nonlinearity, number of variables and uncertain inputs. The results are hereby compared with two state-of-the-art approaches to time-varying uncertainties in nonlinear systems.

Original languageEnglish
Title of host publicationNumerical Software Verification. NSV 2019
Subtitle of host publicationInternational Workshop on Numerical Software Verification
EditorsM. Zamani, D. Zufferey
PublisherSpringer
Pages60-75
Number of pages16
Volume11652
ISBN (Electronic)978-3-030-28423-7
ISBN (Print)978-3-030-28422-0
DOIs
Publication statusPublished - 2019

Publication series

SeriesLecture Notes in Computer Science
Volume11652
ISSN0302-9743

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