DREM procedure application for piecewise constant parameters identification

The research focuses on the applicability of the Dynamic Regressor Extension and Mixing (DREM) procedure for the identification of the piecewise constant parameters of a linear regression. Unlike the known papers, it is shown that the application of the baseline DREM procedure to the identification of piecewise constant parameters generates the scalar perturbed regressions at some time intervals, which significantly deteriorates the quality of the unknown parameters estimates. The methods of the research imply integral and differential calculus and mathematical modeling. To solve the revealed problem, the authors propose a new method of dynamic regressor extension, which is based on the interval integral filtering with exponential forgetting and resetting. The study describes the modified DREM procedure, which, unlike the baseline one, allows one to generate the scalar regressions with an adjustable level of perturbation. Numerical experiments to identify piecewise constant parameters yielded the following results: the correctness of the obtained perturbed regression description and the presence of overshoot of such perturbed regression parameter estimates using the gradient method and FCT-D (Finite Convergence Time DREM). It is also shown that the values of such overshoot can be adjusted if the proposed modified DREM procedure is applied. The proposed procedure can be applied to the development of identification and adaptive control systems.