Modified Finite-Time and Prescribed-Time Convergence Parameter Estimators via the DREM Method

Abstract

This letter proposes a class of modified continuous-time (CT) and discrete-time (DT) finite-time convergence (FTC) estimators based on the dynamic regressor extension and mixing (DREM) method, additionally the same two estimators with alertness preservation and, finally CT and DT prescribed-time convergence (PTC) estimators. In contrast to previously designed FTC estimators based on the DREM method, by introducing the integration and the summation operations, the proposed ones possess the following features: (i) the convergence rate is improved; (ii) the FTC property can be maintained even for a weaker excitation signal. Additionally, the proposed PTC estimators ensure that under certain conditions the estimate converges to the unknown parameter in the prescribed time.