# Towards a performance theory of robust adaptive control

Sanei, A. and French, M. (2004) Towards a performance theory of robust adaptive control. International Journal of Adaptive Control and Signal Processing, 18, (4), 403-421.

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.