Predefined-time parameter estimation via modified dynamic Regressor extension and mixing

Abstract

This paper presents a novel switching predefined-time parameter identification algorithm with a relaxed excitation condition based on the dynamic regressor extension and mixing (DREM) method. DREM often requires the persistent excitation (PE) of the extended square regressor's determinant to ensure exponential parameter convergence. Unlike the classical DREM method, a new parameter identification algorithm configured with a two-layer filter technique is proposed under a relaxed initial excitation (IE) condition, rather than strict PE. A key point in choosing IE instead of PE is the introduction of a smooth switching function that dominates the pure integral action and filter behavior of the extended square regressor. The proposed algorithm relies on the predefined-time stability theorem and the settling-time of the identification algorithm is set a priori as a system parameter. The contributions of this paper are a novel switching predefined-time parameter estimation algorithm that 1) relaxes the stringent PE condition, 2) achieves predefined-time convergence, and 3) guarantees the monotonicity of each element of the parameter error inherited from the classical DREM method. Comparative simulation results are presented to illustrate the effectiveness of the proposed algorithm.