Robust Hybrid Finite-Time Parameter Estimation Without Persistence of Excitation

Abstract

In this paper, we consider the problem of estimating parameters of a linear regression model. Using a hybrid systems framework, a hybrid algorithm is proposed allowing the estimate to converge to the exact value of the unknown parameters in predetermined finite time. Interestingly, we show that for the case of constant parameters, the convergence property of the hybrid algorithm holds while only requiring the regressor to be exciting on a given interval. For the case of piecewise constant parameters, the classical persistency of excitation condition is required to guarantee the convergence. Robustness of the proposed algorithm with respect to measurements noise is analysed. Finally, illustrative examples are provided showing the merits of the proposed approach in terms of scalability and the applicability for the general class of time-varying unknown parameters