A systematic procedure is given For digital computation of a sub-optimal non-linear Feedback controlu = φ(x), |φ| ≤ 1, For a systemx=Ax—Bu + Cw, wherewis Gaussian white noise. The performance criterion is expected quadratic cost relative to the stationary probability distribution ofx. A control of form φ(x) = sat (f'xor sgn (f'x) is obtained, by a combination of dynamic programming and statistical linearization; computation time is a few seconds. Applications are given to design of an eighth-order attitude control and of a second-order tracking system. For the latter system, the elliptic differential equation of dynamic programming is solved by finite differences to yield the true optimal control, and results are compared with those for the sub-optimal control. It is shown finally how the procedure can be modified if the observations of tho stato include additive noise.