Towards a performance theory of robust adaptive control

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 output, 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 if the a priori information on the uncertainty level is sufficiently conservative. The second result shows that the projection controller is superior to the dead-zone controller when the a priori information on the disturbance level is sufficiently conservative. For conceptual clarity the results are presented on a non-linear scalar system with a single uncertain parameter and generalizations are briefly discussed. Copyright # 2004 John Wiley & Sons, Ltd.