Persistency of Excitation in Identification Using Radial Basis Function Approximants

Authors:
A. J. Kurdila;Francis J. Narcowich;Joseph D. Ward
Affiliations:
-;-;-
Venue:
SIAM Journal on Control and Optimization
Year:
1995

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Abstract

In this paper, identification algorithms whose convergence and rate of convergence hinge on the regressor vector being persistently exciting are discussed. It is then shown that if the regressor vector is constructed out of radial basis function approximants, it will be persistently exciting, provided a kind of "ergodic" condition is satisfied. In addition, bounds on parameters associated with the persistently exciting regressor vector are provided; these parameters are connected with both the convergence and rates of convergence of the algorithms involved.