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Zbl 1237.93030
Rykaczewski, Krzysztof
Approximate controllability of differential inclusions in Hilbert spaces. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 5, 2701-2712 (2012). ISSN 0362-546X

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 2000:: *93B05 Controllability
93C15 Control systems governed by ODE
34G25 Evolution inclusions
47N10 Appl. of operator theory in optimization, math. programming, etc.

Keywords: approximate controllability; semilinear differential inclusion; Hilbert space; mild solution; fixed point; multivalued map

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