An adaptive regulation approach in linear systems against exogenous inputs consisting of a linear combination of sinusoids with unknown amplitudes, frequencies and phases is proposed within the framework of Youla parameterized stabilizing controllers. The goal of the developed adaptation algorithm is to search, within the set of weighted Ritz-type Youla parameters, for a controller that yields regulation in the closed-loop system. The proposed approach is applied to an active vibration control problem, and the performance of the developed regulator is illustrated by considering the vibration cancellation against exogenous inputs represented as a linear combination of unknown stationary as well as time-varying sinusoidal disturbances.
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