Approximation of the viability kernel |
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Authors: | Patrick Saint-Pierre |
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Institution: | (1) CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France |
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Abstract: | We study recursive inclusionsx
n+1
G(x
n
). For instance, such systems appear for discrete finite-difference inclusionsx
n+1 G
(x
n) whereG
:=1+F. The discrete viability kernel ofG
, i.e., the largest discrete viability domain, can be an internal approximation of the viability kernel ofK underF. We study discrete and finite dynamical systems. In the Lipschitz case we get a generalization to differential inclusions of the Euler and Runge-Kutta methods. We prove first that the viability kernel ofK underF can be approached by a sequence of discrete viability kernels associated withx
n+1
(xn) where
(x) =x + F(x) + (ML/2)
2. Secondly, we show that it can be approached by finite viability kernels associated withx
h
n+1
(
(x
h
n+1
) +(h) X
h
. |
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Keywords: | Viability kernel Differential inclusions Numerical set-valued analysis |
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