An efficient recursive identification algorithm for multilinear systems based on tensor decomposition

Abstract

There are many important fields involving the multilinear system identification. A great number of parameters to be identified is an important challenge, leading to the need for tensorial decomposition and modeling of such systems. This article is about the parameter estimation of the higher‐order multilinear systems with non‐Gaussian noises and to explore the role of tensor algebra in the multilinear model identification. A high‐dimension system identification problem is reformulated in terms of low‐dimension problems by using the tensorial decomposition technique. Further, applying the multi‐innovation identification theory, the recursive algorithm combining with the logarithmic p‐norms is investigated for multilinear systems with non‐Gaussian noises of low computational complexity. Finally, some simulation results illustrate the effectiveness of the proposed recursive identification method.

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

“…System identification is an important tool to construct the mathematical models from the observed data 1‐5 . The accurate mathematical models are the basis of the implementation of the control strategies 6‐9 . In the area of system identification, much attention has been concentrated on linear systems, nonlinear systems, bilinear systems and so on.…”

“…[1][2][3][4][5] The accurate mathematical models are the basis of the implementation of the control strategies. [6][7][8][9] In the area of system identification, much attention has been concentrated on linear systems, nonlinear systems, bilinear systems and so on. Due to the simple system structure, the parameter estimation methods have been matured for linear systems, such as the recursive identification, 10 the iterative estimation, 11,12 the subspace identification, 13 and the maximum likelihood identification.…”

Filtering‐based multi‐innovation recursive identification methods for input nonlinear systems with piecewise‐linear nonlinearity based on the optimization criterion

“…Considerable efforts have been devoted to modeling, identification, adaptive control, and other aspects of nonlinear systems in industrial production process over the years. Among various existing nonlinear models such as Volterra models, 11,12 bilinear models, 13,14 and so forth, the block‐structured nonlinear models have been widely concerned for their abilities of reflecting nonlinear characteristics simply and efficiently. Such models realize the separation design of the static nonlinear part and the dynamic linear part of the nonlinear system, which can be used to describe many typical industrial processes 15‐17 .…”

Noniterative tensor network‐based algorithm for Volterra system identification

“…For example, the storage cost of a square matrix is typically , which can be prohibitively large as increases. A linear TN called tensor train (TT) or matrix product state (MPS) could reduce the storage cost to approximately , where is the maximal TN‐rank and usually low in practice 15,39,40 . A TN representation for the MIMO Volterra system was proposed in Reference 14.…”

“…A linear TN called tensor train (TT) or matrix product state (MPS) could reduce the storage cost to approximately dn 2 r 2 , where r is the maximal TN-rank and usually low in practice. 15,39,40 A TN representation for the MIMO Volterra system was proposed in Reference 14. The alternating linear scheme (ALS) and the modified ALS (MALS) algorithms were derived therein to compute the TN-cores with low TN-ranks.…”