Dominant richness and improvement of performance of robust adaptive control

Abstract Several recent robust adaptive control schemes guarantee stability and residual tracking errors which are “small” in the mean for any bounded initial conditions, independent of any persistence of excitation condition. Since smallness in the mean does not always guarantee small bounds for the tracking error at steady state, the tracking performance of these robust schemes may not be acceptable. In this paper, we show that the convergence and the tracking performance of these globally stable adaptive control schemes can be considerably improved if the reference input signal is chosen to be dominantly rich. We show that dominantly rich signals maintain a high level of persistence of excitation, relative to the level of the modeling error, which guarantees exponential convergence and small bounds for the tracking and parameter error at steady state.