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-sq uares criterion with a forgetting function. The proposed forgetting functio n depends on two time-varying parameters which play crucial roles in the st ability 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 s howing finite time convergence of the Lyapunov function to a neighbourhood of zero, the size of which depends on the evolution of the time-varying err or terms in the parametric model representation. Copyright (C) 2001 John Wi ley & Sons, Ltd.