Abstract
We investigate discrete approximation of the solution set of an impulsive differential inclusions with not fixed time of impulses (jumps) in finite dimensional Euclidean space. The right-hand side is assumed to be almost upper semi continuous and one sided Lipschitz. The fact that the impulsive times are not fixed posses problems and in the paper we study several variants of the Euler method in case of autonomous and not autonomous systems. The accuracy (in appropriate metric) of all considered variants is \(O(\sqrt{h})\). The results can be applied to impulsive optimal control problems.
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Donchev, T. (2008). Approximation of the Solution Set of Impulsive Systems. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2007. Lecture Notes in Computer Science, vol 4818. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78827-0_34
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DOI: https://doi.org/10.1007/978-3-540-78827-0_34
Publisher Name: Springer, Berlin, Heidelberg
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