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The performance of function approximator based adaptive control designs may scale badly with approximator dimension. For a simple system class, both projection based designs and multiresolution approximation based designs have been shown to have good scaling properties with respect to to linear quadratic (LQ) costs. Here we show that by considering a cost functional with penalties on the control rate, the multiresolution approximatior based design can outperform the projection based design. Generalizations are briefly discussed.