On controllability of semilinear stochastic systems in Hilbert spaces

Abstract

A stochastic linear quadratic optimal control problem which depends on parameter is presented. An approximating control which steers the linear stochastic system from an arbitrary point to a small neighbourhood of an arbitrary point, provided that the linear system is approximately controllable, is found. The approximate controllability of the system by means of the Nussbaum fixed-point theorem is analyzed.