Controllability of neutral functional integrodifferential systems in Banach spaces
Semilinear, neutral functional integrodifferential control systems defined in Banach spaces are considered. Using the Schaefer fixed-point theorem, a sufficient condition for exact relative controllability with unconstrained controls in a given time interval is formulated and proved. In the proof of the main result, methods taken from the theory of semigroups of operators are extensively used. Theoretical considerations are illustrated by the controllability investigations for a partial integrodifferential equation with second-order differential operator. The paper also contains remarks concerning controllability results for infinite-dimensional semilinear control systems. Finally, it should be stressed that similar controllability problems have been recently discussed in the paper [\textit{K. Balachandran} and \textit{J. P. Dauer}, Controllability of Sobolev-type integrodifferential systems in Banach spaces, J. Math. Anal. Appl. 217, 335-348 (1998; Zbl 0927.93015)].
neutral functional integrodifferential control systems
scientific article; zbMATH DE number 1428552
scientific article