Volterra系列
非线性系统
非线性系统辨识
应用数学
Volterra方程
鉴定(生物学)
张量分解
数学
核(代数)
高斯分布
参数统计
系统标识
规范(哲学)
对数
数学优化
计算机科学
张量(固有定义)
数学分析
统计
数据建模
物理
植物
政治学
组合数学
法学
纯数学
生物
数据库
量子力学
作者
Xing Tang,Shihua Tang,Xiaobo Gu
标识
DOI:10.1016/j.jfranklin.2021.11.015
摘要
The Volterra model can represent a wide range of nonlinear dynamical systems . However, its practical use in nonlinear system identification is limited due to the exponentially growing number of Volterra kernel coefficients as the degree increases. This paper considers the identification issue of discrete-time nonlinear Volterra systems and uses a tensorial decomposition called PARAFAC to represent the Volterra kernels which can provide a significant parametric reduction compared with the conventional Volterra model. Applying the multi-innovation identification theory, the recursive algorithm by combining the l 2 -norm is proposed for the PARAFAC-Volterra models with the Gaussian noises . In addition, the multi-innovation algorithm combining with the logarithmic p -norms is investigated for the nonlinear Volterra systems with the non-Gaussian noises. Finally, some simulation results illustrate the effectiveness of the proposed identification methods.
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