DREM

The Dynamic Regressor Extension and Mixing (DREM) is a new technique for parameter estimation with guaranteed performance improvement – with respect to the classical gradient or least-squares estimators – that has proven instrumental in the solution of several open problems in system identification and adaptive control. 

The key idea is twofold. First, a set of linear operators is introduced to obtain filtered regressors (the dynamic regressor extension stage). Second, these instrumental signals are mixed via a nonlinear transformation, which is given by adjugate matrix computation (the mixing stage).  This procedure allows rewriting the original problem of estimation of a vector of parameters as a set of independent scalar problems for each parameter separately. The benefits of this transformation are 
  • the new convergence conditions, which are different from a classic Persistency of Excitation condition;
  • the guaranteed monotonicity of the transients for each of the estimated parameters element-wise.

This procedure was first introduced in the IEEE TAC paper and its Luenberger observer interpretation was reported in the Automatica paper
The DREM tool was successfully applied to:
  • parameters identification for multi-sinusoidal signals [1,2] with improved transients performance;
  • direct model reference adaptive control with the relaxed high-frequency gain sign assumption [1]; 
  • control and estimation for sensorless PMSM drives and electromechanical systems  [1,2, 3, 4];
  • photovoltaic arrays control [1];
  • 2D adaptive visual servo robotics.
A discussion on possible connection of the DREM procedure with the composite learning can be found in this preprint, that is currently submitted to Int. Journal of Robust and Nonlinear Control.