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

Abstract

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 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.

Filtered multi‐innovation‐based iterative identification methods for multivariate equation‐error ARMA systems

“…The proposed parameter estimation algorithms in this paper are based on the identification model in (4). Many identification methods are derived based on the identification models of the systems [41][42][43][44][45][46][47] and these methods can be used to estimate the parameters of other linear systems and nonlinear systems [48][49][50][51][52][53] and can be applied to other fields [54][55][56][57][58][59] such as chemical process control systems.…”

Identification of dual‐rate sampled nonlinear systems based on the cycle reservoir with regular jumps network

“…The proposed parameter estimation algorithms in this paper are based on the identification model in (1). Many identification methods are derived based on such identification models of the systems 33‐39 and these methods can be used to estimate the parameters of other linear systems and nonlinear systems, 40‐46 and can be applied to other fields 47‐53 such as chemical process control and electrical systems. Suppose the value of input weights and feedback weights are both $$$ {r}_i $$$, thus all the elements in $$$ {\boldsymbol{W}}_{in},{\boldsymbol{W}}_{back} $$$ are $$$ {r}_i $$$ and the signs of which are randomly generated.…”

Parameter estimation for a class of time‐varying systems with the invariant matrix

“…51,52 The proposed parameter estimation algorithms in this article are based on the identification model in ( 21)- (20). Many identification methods are derived based on the identification models of the systems [53][54][55][56] and these methods can be used to estimate the parameters of other linear systems and nonlinear systems [57][58][59][60][61][62] and can be applied to other fields such as chemical process control systems.…”