Adaptive control of parametric nonlinear autoregressive models via a new martingale approach

The purpose of this note is to investigate the stability and the optimality of the adaptive tracking for a wide class of parametric nonlinear autoregressive models, via a new martingale approach. Several asymptotic results for the standard least squares estimator of the unknown model parameter, such as a central limit theorem, a law of iterated logarithm, and strong laws of large numbers are also provided.