Second‐order optimization methods for time‐delay Autoregressive eXogenous models: Nature gradient descent method and its two modified methods

Abstract

SummaryThis article proposes several second‐order optimization methods for time‐delay ARX model. Since the time‐delay in the information vector makes the traditional identification algorithms be inefficient, a redundant rule based method is utilized to transformed the model into a redundant model. Then, the nature gradient descent (NGD) algorithm is developed for such a model. To reduce the computational efforts of the NGD algorithm and to adaptively update each element in the parameter vector, two modified NGD algorithms are also presented. The simulation examples verify the effectiveness of the proposed algorithms.