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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 \[ dx=Ax dt+f(t,x) dt+g(t,x)\nu (dx), \;t\geq 0, \;x(0)=x_0. \tag{1} \] Problem (1) is considered in a Banach space \(E\). Here, \(A\) is the infinitesimal generator of a \(C_0\)-semigroup \(\{S(t)\}_{t\geq 0}\) 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 differential equations in abstract spaces
34A37 Ordinary differential equations with impulses
34G25 Evolution inclusions
49J27 Existence theories for problems in abstract spaces
93B52 Feedback control
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