Approximation of the viability kernel |
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Authors: | Patrick Saint-Pierre |
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Affiliation: | (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 inclusionsxn+1 G(xn). For instance, such systems appear for discrete finite-difference inclusionsxn+1 G(xn) 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 withxn+1 (xn) where(x) =x + F(x) + (ML/2) 2. Secondly, we show that it can be approached by finite viability kernels associated withxhn+1 ((xhn+1) +(h) Xh. |
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Keywords: | Viability kernel Differential inclusions Numerical set-valued analysis |
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