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

Ahmed, N. U.

Publ. Math. Debr. 70, No. 3-4, 371-393 (2007).

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.

Reviewer: Jozef Banaś (Rzeszow)

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

Keywords:

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