Controllability of semilinear control systems dominated by the linear part. (English) Zbl 0617.93004

The author shows the approximate controllability of the abstract semilinear control system \(y_ t+Ay(t)=F(y(t))+(Bv)(t)\), \(y(0)=0\), \(0<t<T\), under simple fundamental assumptions on the system components. In particular, range conditions on the mapping B are imposed. This is illustrated by two examples.
Reviewer: K.Werner


93B05 Controllability
93C10 Nonlinear systems in control theory
93C25 Control/observation systems in abstract spaces
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
47D03 Groups and semigroups of linear operators
93B03 Attainable sets, reachability
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