Comments on -adaptive control: stabilisation mechanism, existing conditions for stability and performance limitations

Abstract

In recent years, we have witnessed the publication in various control and applications journals of some papers where it is suggested to replace the tracking error-driven parameter estimator of direct model reference adaptive controller with a state prediction-driven one, used in indirect schemes. Moreover, it is suggested to compute the controller with a linear time-invariant filter and to use high adaptation gains. It has been claimed that these modifications improve the performance of the system. The objective of this paper is to discuss these claims with the simplest possible examples. The main contributions of the paper are, first, to reveal that the stabilisation mechanism is univocally determined by the filter and is independent of the parameter adaptation. Second, to prove that the condition for stability suggested in the literature cannot be verified, even in basic examples. Finally, to prove that the controller cannot ensure suitable tracking (or regulation) performance even for these examples.