Naito, Koichiro Controllability of semilinear control systems dominated by the linear part. (English) Zbl 0617.93004 SIAM J. Control Optimization 25, 715-722 (1987). 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 Cited in 1 ReviewCited in 133 Documents MSC: 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 Keywords:approximate controllability; semilinear control system; range conditions PDFBibTeX XMLCite \textit{K. Naito}, SIAM J. Control Optim. 25, 715--722 (1987; Zbl 0617.93004) Full Text: DOI