A Comparison Between Two Robust Adaptive Controllers w.r.t a Non–singular Transient Cost

A nonsingular performance comparison between two standard robust adaptive control designs based on the dead-zone and projection modifications is given. A worst case transient cost functional penalising the L∞ norm of the state, control and control derivative has been chosen as the criterion of comparison. 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 clarity of the presentation, the result is restricted to scalar systems and the generalisations are only briefly discussed.