We develop an algorithm to control an unknown nonlinear fading memory discrete-time system, Our approach is based on nonparametric regression techniques rather than traditional feedback control, We discuss a procedure that, given a desired periodic output and a tolerance, produces an acceptable output from any system in a wide class. The algorithm uses as data past inputs (which are selected by the algorithm) and corresponding (possibly noisy) output observations and needs no extra parametric knowledge or restrictions on the system, We also present an algorithm that produces an output that converges to the desired output when stricter conditions are imposed on the system, Our approach, in its current form, however, cannot be used to control open-loop unstable systems.