A non-singular performance comparison between two robust adaptive control designs

We consider standard robust adaptive control designs based on the dead-zone and projection modifications, and compare their performance w.r.t. a worst case transient cost functional penalizing the L^∞ norm of the state, control and control derivative. If a bound on the L^∞ norm of the disturbance is known, it is shown that the dead-zone controller outperforms the projection controller when the a-priori information on the unknown system parameter is sufficiently conservative. For simplicity the results are presented for a scalar system and generalizations are briefly discussed