- Tytuł:
- Viability and generalized differential quotients
- Autorzy:
-
Girejko, E.
Bartosiewicz, Z. - Powiązania:
- https://bibliotekanauki.pl/articles/970016.pdf
- Data publikacji:
- 2006
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
viability
differential inclusion
generalized differential quotient (GDQ)
contingent derivative
Cellina continuous approximability (CCA) - Opis:
- Necessary and sufficient conditions for a set-valued map K : R → Rn to be GDQ-differentiable are given. It is shown that K is GDQ differentiate at to if and only if it has a local multiselection that is Cellina continuously approximable and Lipschitz at to. It is also shown that any minimal GDQ of K at (to,yo) is a subset of the contingent derivative of K at (to,yo), evaluated at 1. Then this fact is used to prove a viability theorem that asserts existence of a solution to the initial value problem y(t) ∈ F(t, y(t)), with y(to) =yo, where F : Gr(K) → Rn is an orientor field (i.e. multivalued vector field) defined only on the graph of K and K : T → Rn is a time-varying constraint multifunction. One of the assumptions is GDQ differentiability of K.
- Źródło:
-
Control and Cybernetics; 2006, 35, 4; 815-829
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł