A Simple Adaptive Control Algorithm with Adaptive Supplementary Dynamics

A new implementation is proposed for 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). Our new implementation inserts supplementary dynamics in a feedback path which is inside the adaptive mechanism. The matrices (Af, Bf, Cf, Df) which define the supplementary dynamics are computed on-line as part of the adaptive gain computations. Therefore, this new implementation differs from other CGT adaptive control algorithms which require the implementation of the inverse of a known stabilizing compensator in parallel with the plant such that the augmented plant is ASPR. We require knowledge of a lower bound on the ordar of stabilizing compensator for the controllable and observable plant and the satisfaction of some mild sufficient conditions. An example is presented which of an unstable single-input single-output plant.