Approximate controllability of second order integrodifferential systems
Global approximate controllability in a given time-interval of a semilinear integrodifferential second-order dynamical system is considered. It is generally assumed that the dynamical system is defined in an infinite-dimensional Banach space, and that it contains both a linear and a nonlinear part. Using the theory of linear semigroups of bounded operators and fixed point theorems, a sufficient condition for approximate global controllability is formulated and proved. As an application, approximate global controllability of certain second-order semilinear distributed parameter system with Dirichlet type boundary conditions is investigated. Similar controllability problems have been recently considered in the paper of the first two authors [J. Math. Anal. Appl. 230, No. 1, 242-250 (1999; Zbl 0917.93009)].
semilinear integrodifferential second-order dynamical systems
scientific article; zbMATH DE number 1281620