A new procedure to design parameter estimators for linear and nonlinear regressions, called dynamic regressor extension and mixing (DREM), was recently proposed. A key feature of DREM is that it transforms the problem of estimation of an q-dimensional parameter vector into the estimation of q decoupled, scalar parameters. The technique has been successfully applied in a variety of identification and adaptive control problems. The connection of DREM with classical functional Luenberger observers for time-varying systems was recently established.

In this talk it is shown that, using the DREM technique, it is possible to remove two key assumptions imposed in adaptive control of linear time-invariant multivariable systems. First, for model reference adaptive control, we obviate the need of any prior knowledge on the high frequency gain. For the case of scalar systems this is tantamount to removing the requirement of known sign of this coefficient. Second, we present an adaptive pole-placement scheme that avoids the appearance of singularities that may appear in the calculation of the controller parameters, without appealing to persistency of excitation assumptions nor the use of projections. Besides the use of the new parameter estimator, the only modifications introduced to these classical controller structures are a parameter shifting and a scaling factor that—under suitable excitation assumptions—disappear recovering in this way, the standard schemes.

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