Approximate controllability of semilinear functional equations in Hilbert spaces. (English) Zbl 1017.93019

Approximate and complete controllability for semilinear functional differential systems in Hilbert spaces is studied. Sufficient conditions are established for each of these types of controllability. The results address the limitation that linear systems in infinite-dimensional spaces with compact semigroup cannot be completely controllable. The conditions are obtained by using the Schauder fixed point theorem when the semigroup is compact and the Banach fixed point theorem when the semigroup is not compact.


93B05 Controllability
93C25 Control/observation systems in abstract spaces
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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