Persistency of excitation in identification using radial basis function approximants. (English) Zbl 0831.93015

Kurdila, A. J.; Narcowich, Francis J.; Ward, Joseph D.

SIAM J. Control Optimization 33, No. 2, 625-642 (1995).

Identification algorithms requiring persistent excitation for convergence are discussed. The use of radial basis functions to construct the regressor vector is investigated and in this case, the persistency of excitation is shown to be achieved under some conditions which the authors call “ergodic”. The convergence of the least squares algorithm and of a gradient descent method with dead zone are shown. In the case of Gaussian radial basis functions, bounds on parameters associated with convergence and convergence rates are obtained.

Reviewer: E.Bose (Durban)

MSC:

93B30	System identification
41A30	Approximation by other special function classes

Keywords:

identification algorithms; persistent excitation; radial basis functions