Optimal adaptive controller based on the ELS algorithm is established using the input matching technique. The control signal is reduced to a constant weighted sum of the measurable information-state vector components using a one-step-ahead quadratic cost function to govern the behavior of the stochastic linear systems. The control effort can be estimated globally. The algorithm also predicts the convergence rate. With no excitation condition, the closed-loop system is globally stable and the input converges to the one-step-ahead optimal input.