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Optimal feedback control for impulsive systems on the space of finitely additive measures. (English) Zbl 1164.34026
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.

34G20Nonlinear ODE in abstract spaces
34A37Differential equations with impulses
34G25Evolution inclusions
49J27Optimal control problems in abstract spaces (existence)
93B52Feedback control