Adaptive control of linear multivariable systems using dynamic regressor extension and mixing estimators: Removing the high-frequency gain assumptions

Abstract

In this paper it is shown that, using the recently introduced dynamic regressor extension and mixing parameter estimation technique, it is possible to remove the key assumption of prior knowledge on the high frequency gain imposed in model reference adaptive control of linear time-invariant multivariable systems. For the case of scalar systems this is tantamount to removing the requirement of known sign of this coefficient. The proposed controller is not certainty equivalent in the sense that the parameters generated by the new estimator are not directly applied to the controller, but they are modified adding a shifting and a scaling factor. Under the weak assumption of interval excitation, parameter convergence in finite time of the modified parameters is achieved, ensuring good robustness of the proposed controller.