# zbMATH — the first resource for mathematics

Approximate controllability of semilinear delay control systems. (English) Zbl 1141.93016
Summary: Approximate controllability of an abstract semilinear delay control system of the form
$x'(t)= Ax(t)+ Bu(t)+ f(t,x(t+\theta), u(t)),$
where $$0<t\leq T$$ and $$-h\leq\theta\leq 0$$ is proved under simple sufficient conditions on the system operators $$A$$, $$B$$ and $$f$$. The result is illustrated with semilinear controlled heat equation.

##### MSC:
 93B05 Controllability 93C25 Control/observation systems in abstract spaces 93C10 Nonlinear systems in control theory