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le 12 novembre 2020

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Khalil Ghorbal

LAMPS LOGO
Jeudi 12 novembre 2020 à 11h15
Khalil Ghorbal
INRIA de Rennes
Titre : Characterizing Positively Invariant Sets: Inductive and Topological Methods
 
Abstract: Set positive invariance is an important concept in the theory of dynamical systems and one which also has practical applications in areas of computer science, such as formal verification, as well as in control theory. Great progress has been made in understanding positively invariant sets in continuous dynamical systems and powerful computational tools have been developed for reasoning about them; however, many of the insights from recent developments in this area have largely remained folklore and are not elaborated in existing literature. This presentation contributes an explicit development of modern methods for checking positively invariant sets of ordinary differential equations and describes two possible characterizations of positive invariants: one based on the real induction principle, and a novel alternative based on topological notions. The two characterizations, while in a certain sense equivalent, lead to two different decision procedures for checking whether a given semi-algebraic set is positively invariant under the flow of a system of polynomial ordinary differential equations. This is a joint work with Andrew Sogokon from University of Southampton, UK.

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Mise à jour le 9 novembre 2020