Enhanced Parameter Convergence for Linear Systems Identification: The DREM Approach

Dynamic regressor extension and mixing is a new technique for parameter estimation that has proven instrumental in the solution of several open problems in system identification and adaptive control. A key property of the estimator is that, for linear regression models, it guarantees monotonicity of each element of the parameter error vector that is a much stronger property than monotonicity of the vector norm, as ensured with classical gradient or least-squares estimators. On the other hand, the overall performance improvement of the estimator is strongly dependent on the suitable choice of certain operators that enter in the design. In this paper we investigate the impact of these operators on the convergence properties of the estimator in the context of identification of linear time-invariant systems. In particular, we give some guidelines for their selection to ensure convergence under the same (persistence of excitation) conditions as standard identification schemes.