Robustness of the tuning functions adaptive backstepping design for linear systems

A new approach to adaptive control of linear systems which abandons the certainty-equivalence principle has been recently developed in the ideal case, that is, in the absence of unmodeled dynamics and bounded disturbances. In this paper the authors address the question of robustness and asymptotic performance of this adaptive scheme. The authors show that using a switching /spl sigma/-modification in the parameter update law, the closed loop system states are uniformly ultimately bounded with a region of attraction inversely proportional to the "size" of the unmodeled dynamics. The tracking error is shown to be proportional to the size of the uncertainties.