ON CONTROLLABILITY OF INFINITE DIMENSIONAL LINEAR STOCHASTIC SYSTEMS

The controllability problem for linear dynamical systems forced by additive stochastic disturbances is considered. The control system is modeled by an abstract evolution equation on a Hilbert space and the stochastic forcing term of a highly general type is modeled by a Hilbert space-valued semimartingale. The initial control problem is reduced to a special optimal stochastic control problem which is investigated by means of the convex extremum problems duality theory. A duality principle is established from which the stochastic controllability criterion is deduced and it allows to obtain a relation between stochastic controllability and deterministic controllability of the corresponding undisturbed system. For the systems where the stochastic disturbances have only a martingale component the property of stochastic controllability is preserved in the class of linear feedback controls.