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### A generalization of Graves' Theorem with a closed convex set as a constraint

 Citace: CIBULKA, R. A generalization of Graves' Theorem with a closed convex set as a constraint. Kamenice pod Lipou, 2008. PŘEDNÁŠKA, POSTER eng A generalization of Graves' Theorem with a closed convex set as a constraint 2008 Kamenice pod Lipou Radek Cibulka Dokazujeme zobecnění známé Gravesovy věty a ilustrujeme její použití pro zkoumání nelineárních dynamických systémů s omezeními. We prove a generalization of well-known Graves' Theorem and use it in consideration of an infinite-dimensional dynamical system described by a nonlinear abstract differential equation. The controls are subject to constraints given by a closed convex subset of $L^\infty([0,T],U)$, where $U$ is a real Banach space and $T > 0$. Using a generalized Graves theorem, sufficient conditions for constrained exact local controllability in time $T$ are proved.

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