Towards a performance theory of robust adaptive control

Abstract

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 penalising the $L^\infty$ norm of the output, control and control derivative. If a bound on the $L^\infty$ 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 nonlinear scalar system with a single uncertain parameter and generalisations are briefly discussed.

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