Convergence Properties of Some Recursive Identification Schemes and Adaptive Predictors

By making use of martingale theory, we have recently established the convergence of several recursive identification schemes under minimal assumptions on the inputs. We no longer require the inputs to be persistently exciting; moreover, the system can be allowed to be unstable and the results are applicable to general feedback systems. Herein we briefly summarize these convergence results. More importantly, even when these recursive identification schemes fail to converge, our approach also provides precise estimates concerning the performance of certain adaptive predictors based on the identification schemes.