Overall recursive least squares and overall stochastic gradient algorithms and their convergence for feedback nonlinear controlled autoregressive systems

This article deals with the problems of the parameter estimation for feedback nonlinear controlled autoregressive systems (i.e., feedback nonlinear equation-error systems). The bilinear-in-parameter identification model is formulated to describe the feedback nonlinear system. An overall recursive least squares algorithm is developed to handle the difficulty of the bilinear-in-parameter. For the purpose of avoiding the heavy computational burden, an overall stochastic gradient algorithm is deduced and the forgetting factor is introduced to improve the convergence rate. Furthermore, the convergence analysis of the proposed algorithms are established by means of the stochastic process theory. The effectiveness of the proposed algorithms are illustrated by the simulation example.