Adaptive regulation for minimum phase systems with unknown relative degree and uncertain exosystems

Abstract

This paper investigates the adaptive error feedback regulation problem for unknown minimum phase, single-input, single-output linear systems with uncertain exosystems. The design problem of a feedback control which is capable of driving the output tracking error exponentially to zero, on the basis of the output tracking error only, is locally solved by an adaptive controller which continuously updates the frequency estimates and requires only two informations on the uncertain linear system: (i) an upper bound for the relative degree; (ii) the sign of the high-frequency gain. The proposed adaptive controller contains two gains to be tuned: an adaptation gain which should be chosen sufficiently small and a control gain which should be chosen sufficiently large. Extensions to single-input single-output nonlinear systems affected by uncertain biased multisinusoidal disturbances are outlined.