Generalized forgetting functions for on-line least-squares identification of time-varying systems

The problem of on-line identification of a parametric model for continuous-time, time-varying systems is considered via the minimization of a least-squares criterion with a forgetting function. The proposed forgetting function depends on two time-varying parameters which play crucial roles in the stability analysis of the method. The analysis leads to the consideration of a Lyapunov function for the identification algorithm that incorporates both prediction error and parameter convergence measures. A theorem is proved showing finite time convergence of the Lyapunov function to a neighbourhood of zero, the size of which depends on the evolution of the time-varying error terms in the parametric model representation.