Design of an adaptive control observer which implicitly specifies a reference model

An algorithm is proposed for adaptive control of a linear plant with unknown constant parameters, only the plant input and output being measurable. The control goal is to make the plant outputs and those of an implicity specified reference model to coincide. The plant description and (observation) controller structure are chosen so that unknown plant parameters coincide with the “desired” values of the controller parameters. Therefore the controller parameters are adjusted through an adaptive observation algorithm which acts in closed loop. For convergence of the controller parameters to the desired values the frequency spectrum of the system input signal can be enriched in the transient process. Differential inequalities help prove stability of the control algorithm.