A unified theory for the CGT approach to adaptive control

Abstract

The command generator tracker (CGT) approach to model reference adaptive control of linear time invariant multi-input multi-output plants which are not almost strictly positive real (ASPR) is considered. Three new algorithms are proposed which are characterized by the insertion of supplementary dynamics in (i) feedback with the plant; (ii) in parallel with the plant; and (iii) in cascade with the plant, respectively. The three different implementations are shown to be special cases of a metasystem representation for the adaptive system. The new algorithms extend earlier results by introducing adaptive gains for the supplementary dynamics in addition to adaptive gains for the controller. A stability proof is presented which shows that the error between the plant and model outputs is bounded in the presence of bounded input and output disturbances. If the model input is constant for t ≥ t 1, and no disturbances exist, then conditions are obtained for the choice of the design parameters in the parallel supplementary dynamics case which guarantee that the output error is asymptotically vanishing.