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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
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