A learning control solution to the problem of finding a finite-time optimal control history that minimizes a quadratic cost is presented. Learning achieves optimization without requiring detailed knowledge of the system, which may be affected by unknown but repetitive disturbances. The optimal solution is synthesized one basis function at a time, reaching optimality in a finite number of trials. These system-dependent basis functions are special in that (1) each newly added basis function is learned without interfering with the previously optimized ones, and (2) it is extracted using data from previous learning trials. Numerical and experimental results are used to illustrate the algorithm.