Unification of some continuous-time adaptive control schemes

Model reference adaptive regulators based on input-output descriptions are examined. By reinterpreting the concept of "augmented error," it is shown that there are no essential differences between the model reference adaptive algorithms and the self-tuning regulators. Both types of schemes can be thought of as composed of a parameter estimator and a control law, based on the parameter estimates. It is shown that many schemes proposed are special cases of a general algorithm. The positive real condition for model reference adaptive systems is also examined. It is shown that this condition is a consequence of the choice of the estimator and that it is not crucial for stability.