  An infinite-dimensional bilinear optimal control problem with infinite-time
horizon is considered. The associated value function can be expanded in a
Taylor series around the equilibrium, the Taylor series involving multilinear
forms which are uniquely characterized by generalized Lyapunov equations. A
numerical method for solving these equations is proposed. It is based on a
generalization of the balanced truncation model reduction method and some
techniques of tensor calculus, in order to attenuate the curse of
dimensionality. Polynomial feedback laws are derived from the Taylor expansion
and are numerically investigated for a control problem of the Fokker-Planck
equation. Their efficiency is demonstrated for initial values which are
sufficiently close to the equilibrium.
