论文标题
具有正则张量网络B-Splines的非线性系统识别
Nonlinear system identification with regularized Tensor Network B-splines
论文作者
论文摘要
本文介绍了使用非线性自动回收外源性（NARX）方法对非线性系统进行正则识别的张量网络B-Spline模型。张量网络理论用于通过将高维重量张量表示为低级别近似值来减轻多元B-splines的维度的诅咒。开发了基于基于交替线性方案的迭代算法，以直接估计低量张量网络近似，从而消除了明确构建指数型大的重量张量的需求。这可以显着降低计算和存储复杂性，从而识别具有大量输入和滞后的NARX系统。所提出的算法在数值上是稳定的，对噪声的稳定性，可以单调地收敛，并可以直接融合正规化。 TNBS-NARX模型通过识别级联的水务基准非线性系统验证，在该基准非线性系统上，它可以在该系统上实现最新性能，同时在标准台式计算机上识别4秒钟的16维B-Spline表面。 GitHub上提供了开源MATLAB实现。
This article introduces the Tensor Network B-spline model for the regularized identification of nonlinear systems using a nonlinear autoregressive exogenous (NARX) approach. Tensor network theory is used to alleviate the curse of dimensionality of multivariate B-splines by representing the high-dimensional weight tensor as a low-rank approximation. An iterative algorithm based on the alternating linear scheme is developed to directly estimate the low-rank tensor network approximation, removing the need to ever explicitly construct the exponentially large weight tensor. This reduces the computational and storage complexity significantly, allowing the identification of NARX systems with a large number of inputs and lags. The proposed algorithm is numerically stable, robust to noise, guaranteed to monotonically converge, and allows the straightforward incorporation of regularization. The TNBS-NARX model is validated through the identification of the cascaded watertank benchmark nonlinear system, on which it achieves state-of-the-art performance while identifying a 16-dimensional B-spline surface in 4 seconds on a standard desktop computer. An open-source MATLAB implementation is available on GitHub.
