Reachability Analysis of Nonlinear ODEs Using Polytopic Based Validated Runge-Kutta

Julien Alexandre dit Sandretto, Jian Wan

Research output: Chapter in Book/Published conference outputConference publication


Ordinary Differential Equations (ODEs) are a general form of differential equations. This mathematical format is often used to represent the dynamic behavior of physical systems such as control systems and chemical processes. Linear ODEs can usually be solved analytically while nonlinear ODEs may need numerical methods to obtain approximate solutions. There are also various developments for validated simulation of nonlinear ODEs such as explicit and implicit guaranteed Runge-Kutta integration schemes. The implicit ones are mainly based on zonotopic computations using affine arithmetics. It allows to compute the reachability of a nonlinear ODE with a zonotopic set as its initial value. In this paper, we propose a new validated approach to solve nonlinear ODEs with a polytopic set as the initial value using an indirectly implemented polytopic set computation technique.
Original languageEnglish
Title of host publicationReachability Problems
Subtitle of host publication12th International Conference, RP 2018, Marseille, France, September 24-26, 2018
EditorsIgor Potapov, Pierre-Alain Reynier
ISBN (Electronic)9783030002503
ISBN (Print)9783030002497
Publication statusPublished - 30 Aug 2018

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


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