Modeling nonlinear systems using the tensor network B‐spline and the multi‐innovation identification theory

Abstract

AbstractThe nonlinear autoregressive exogenous (NARX) model shows a strong expression capacity for nonlinear systems since these systems have limited information about their structures. However, it is difficult to model the NARX system with a relatively high dimension by using the popular polynomial NARX and the neural network efficiently. This article uses the tensor network B‐spline (TNBS) to model the NARX system, whose representation of the multivariate B‐spline weight tensor can alleviate the computation and store burden for processing high‐dimensional systems. Furthermore, applying the multi‐innovation identification theory and the hierarchical identification principle, the recursive algorithm by combining the ‐norm is proposed to the NARX system with Gaussian noise. Because of the local adjustability of the B‐spline curve, the TNBS can fit nonlinear systems with strong nonlinearity by the meaning of setting a proper degree and knots number. Finally, a numerical experiment is given to demonstrate the effectiveness of the proposed algorithm.