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Zbl 1164.34026
Ahmed, N.U.
Optimal feedback control for impulsive systems on the space of finitely additive measures.
(English)
[J] Publ. Math. 70, No. 3-4, 371-393 (2007). ISSN 0033-3883

The paper deals with the existence of measure solutions of the initial value problem for the evolution equation of the form $$dx=Ax dt+f(t,x) dt+g(t,x)\nu (dx), \;t\ge 0, \;x(0)=x_0. \tag{1}$$ Problem (1) is considered in a Banach space $E$. Here, $A$ is the infinitesimal generator of a $C_0$-semigroup $\{S(t)\}_{t\ge 0}$ on $E$. Moreover, $f,g:[0,T]\times E\to E$ are measurable functions and $\nu$ is a signed measure. The existence of measure solutions of differential inclusions is also investigated.
[Jozef Banaś (Rzeszow)]
MSC 2000:
*34G20 Nonlinear ODE in abstract spaces
34A37 Differential equations with impulses
34G25 Evolution inclusions
49J27 Optimal control problems in abstract spaces (existence)
93B52 Feedback control

Keywords: semigroups of operators; semilinear equations; measurable vector fields; finitely additive measures; measure solutions; differential equations and inclusions on space of measures; optimal control

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