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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 ℒ︁∞ norm of the output, control and control derivative. If a bound on the ℒ︁∞ 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.