Parameter convergence of modified adaptive laws with persistent excitation

Abstract

The effect of σ-modification on the parameter convergence and stability properties of two different adaptive laws is analyzed. It is shown that σ-modification does not alter the ideal convergence properties of the adaptive laws without modifications, but instead improves the rate of parameter convergence when the error is large. Furthermore, it does not interfere with the persistence excitation (PE) property of the information signal vector in any adverse way. The effect of the dead zone and other modifications on parameter convergence in the presence of PE signals is not included.