Generalized continuous mixed p‐norm based sliding window algorithm for a bilinear system with impulsive noise

Abstract

This article investigates the identification issue of the bilinear system in the presence of the impulsive noise. The bilinear system based on the observer canonical form is translated into a regressive form, and a bilinear state observer is established to estimate the state variables. To overcome the effects of the impulsive noise to parameter estimation, the proposed algorithms employ a generalized continuous mixed p$$ p $$‐norm cost function, which can generate an adjustable gain that control the proportions of the error norms without resorting to a priori knowledge of the noise. Moreover, a sliding window is designed to update the dynamical data by removing the oldest data and adding the newest measurement data. An numerical example exhibits that the proposed algorithms can reduce the impact of the impulsive noise to parameter estimation and improve the parameter estimation accuracy compared with the conventional algorithms.

Hierarchical estimation methods based on the penalty term for controlled autoregressive systems with colored noises

“…Identification methods can be derived through solving an optimization problem such as minimizing some criterion functions about the squared sum of the differences between the system outputs and the model outputs. Recently, many identification methods have been proposed for linear systems, 12 time-varying system, 13 bilinear systems 14 and nonlinear systems. [15][16][17] The objective function of machine learning algorithms is empirical risk plus structural risk.…”

Expectation‐maximization algorithm for bilinear state‐space models with time‐varying delays under non‐Gaussian noise

“…[4][5][6] Furthermore, the bilinear system can theoretically approximate a class of input-affine dynamic system and is more accurate than traditional linear approximation. [7][8][9] Thus, the research on the identification algorithm of bilinear SSM has high academic value.…”

“…As a particular kind of nonlinear system, the bilinear SSM contains the coupled term of the state vector and the control vector, and has an obvious changeable structure, which can describe the nuclear reaction process, population evolution process, cell division, and others 4‐6 . Furthermore, the bilinear system can theoretically approximate a class of input‐affine dynamic system and is more accurate than traditional linear approximation 7‐9 . Thus, the research on the identification algorithm of bilinear SSM has high academic value.…”

Parameter and order estimation algorithms and convergence analysis for lithium‐ion batteries

“…In order to enhance the identification performance, some improved GD algorithms have proposed by introducing the forgetting factor, the momentum term, the weighted factor and so on. By designing a new search direction or calculating the best step size, the algorithm achieves a better accurate parameter estimation 42‐44 . The recursive methods can real‐timely estimate the parameters of the systems and are suitable for on‐line identification through capturing the real‐time information from actual production processes 45‐51 .…”

“…By designing a new search direction or calculating the best step size, the algorithm achieves a better accurate parameter estimation. [42][43][44] The recursive methods can real-timely estimate the parameters of the systems and are suitable for on-line identification through capturing the real-time information from actual production processes. [45][46][47][48][49][50][51] In contrast, the iterative methods update the parameters of the systems through using a batch of measurement data and are suitable for off-line identification.…”