An Algorithm for Viability Kernels in Hoelderian Case: Approximation by Discrete Dynamical Systems

Quincampoix, M. & Saint-Pierre, P. (1993). An Algorithm for Viability Kernels in Hoelderian Case: Approximation by Discrete Dynamical Systems. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-93-057

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Abstract

In this paper, we study two new methods for approximating the viability kernel of a given set for a Holderian differential inclusion. We approximate this kernel by viability kernels for discrete dynamical systems. We prove a convergence result when the differential inclusion is replaced by a sequence of recursive inclusions. Furthermore, when the given set is approached by a sequence of suitable finite sets, we prove our second main convergence result. This paper is the first step to obtain numerical methods.

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