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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 (extended version) and its Luenberger observer interpretation was reported in the Automatica paper(available here). 
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];
  • estimation of power system inertia [1];
  • photovoltaic arrays control [1];
  • 2D adaptive visual servo robotics [1].

The ongoing research includes:
  • a discussion on possible connections of the DREM procedure with the composite learning (accepted, to appear in Int. Journal of Robust and Nonlinear Control in 2019, the preprint is available);
  • finite-time and fixed-time convergence in DREM under weak excitation conditions.