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Controllability of functional semilinear integrodifferential systems in Banach spaces. (English) Zbl 0982.93018
Semilinear functional integrodifferential control systems defined in infinite-dimensional Banach spaces are considered. Using the Schaefer fixed-point theorem and methods of nonlinear functional analysis, sufficient conditions for global exact controllability in a given time interval and with unconstrained controls are formulated and proved. An illustrative example taken from the theory of parabolic type partial functional integrodifferential control systems is presented and controllability conditions are established. It should be pointed out that in all controllability conditions, exact controllability of the linear part of the semilinear system is required. Moreover, several remarks and comments concerning fixed-point methods in controllability investigations are given. Finally, it should be mentioned that similar controllability problems have been recently considered in the paper [K. Balachandran and J. P. Dauer, Controllability of Sobolev-type integrodifferential systems in Banach spaces, J. Math. Anal. Appl. 217, 335-348 (1998; Zbl 0927.93015)].
93C25Control systems in abstract spaces
93C23Systems governed by functional-differential equations
93C10Nonlinear control systems