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

• Published in: International journal of robust and nonlinear control Vol. 32; no. 13; pp. 7304 - 7318
• Main Authors: Wang, Yanjiao, Tang, Shihua, Deng, Muqing
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.09.2022
• Subjects: Algorithms; Autoregressive models; B‐spline; Innovations; Mathematical analysis; multi‐innovation identification theory; NARX system; Neural networks; Nonlinear systems; Nonlinearity; online identification; Polynomials; Random noise; Spline functions; tensor network; Tensors
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.6221

The 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 l2$$ {l}_2 $$‐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.