Compactly supported orthogonal wavelets have certain properties that are useful for system identification and learning control. Drawing on the rich theory of wavelets, we propose a system identification scheme based on orthogonal wavelets. Better accuracy of estimation can be obtained by adding more terms to the wavelet based identifier, and these terms do not alter the coefficients of the existing terms. These terms can be selectively added depending upon the region of interest, for example we may require more terms in regions where the identified functions vary rapidly. We illustrate the concepts by applying the procedure to determine a speed-controller for an electric vehicle.