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Approximate controllability of differential inclusions in Hilbert spaces. (English) Zbl 1237.93030
Summary: In this paper, controllability for the system originating from semilinear functional differential equations in Hilbert spaces is studied. We consider the problem of approximate controllability of semilinear differential inclusion assuming that semigroup, generated by the linear part of the inclusion, is compact and under the assumption that the corresponding linear system is approximately controllable. By using the resolvent of the controllability Gramian operator and a fixed-point theorem, sufficient conditions have been formulated and proved. An example is presented to illustrate the utility and applicability of the proposed method.
##### MSC:
 93B05 Controllability 93C15 Control systems governed by ODE 34G25 Evolution inclusions 47N10 Applications of operator theory in optimization, convex analysis, programming, economics
##### References:
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