Persistent Excitation is Unnecessary for On-line Exponential Parameter Estimation: A New Algorithm that Overcomes this Obstacle

Abstract

In this paper, we prove that it is possible to estimate online the parameters of a classical vector linear regression equation Y= , where Y R^n,\; R^n q are bounded, measurable signals and R^q is a constant vector of unknown parameters, even when the regressor is not persistently exciting. Moreover, the convergence of the new parameter estimator is global and exponential and is given for both continuous-time and discrete-time implementations. As an illustration example, we consider the problem of parameter estimation of a linear time-invariant system, when the input signal is not sufficiently exciting, which is known to be a necessary and sufficient condition for the solution of the problem with the standard gradient or least-squares adaptation algorithms.

Tasks

Reproductions