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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.

##### MSC:
 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