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Controllability of stochastic Volterra integrodifferential systems. (English) Zbl 1031.93039
Nonlinear, stochastic integrodifferential Volterra control systems are considered. It is generally assumed that the systems are defined in infinite-dimensional Banach spaces and that the values of control are unconstrained. Using a contraction mapping principle, sufficient conditions for exact controllability in a given time interval are formulated and proved. In the proofs, methods of nonlinear functional analysis and semigroup theory are extensively used. A simple example of the exact controllability of a stochastic heat equation with integral perturbation is presented. Moreover, several remarks comments and relations to results known in the literature are also given. Finally, it should be pointed out that similar stochastic controllability problems have been considered in the paper [P. Balasubramaniam and J. P. Dauer, J. Appl. Math. Stochastic Anal. 14, 329-339 (2001; Zbl 1031.93040)] reviewed below.

93B05 Controllability
93C25 Control/observation systems in abstract spaces
93E03 Stochastic systems in control theory (general)
93C10 Nonlinear systems in control theory
45R05 Random integral equations
45D05 Volterra integral equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
45G10 Other nonlinear integral equations
Zbl 1031.93040