  In 1961 E. G. Albrekht presented a method for the optimal stabilization of
smooth, nonlinear, finite dimensional, continuous time control systems. This
method has been extended to similar systems in discrete time and to some
stochastic systems in continuous and discrete time. In this paper we extend
Albrekht's method to the optimal stabilization of some smooth, nonlinear,
infinite dimensional, continuous time control systems whose nonlinearities are
described by Fredholm integral operators.
