An innovative parameter estimation for fractional-order systems in the presence of outliers

Cui, Rongzhi; Wei, Yiheng; Chen, Yuquan; Cheng, Songsong; Wang, Yong

doi:10.1007/s11071-017-3464-7

Cited by 36 publications

(12 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where () uk is the output of the static nonlinear link, and it can be represented as: . When the fractional orders of the denominator polynomial and the numerator polynomial in (8) are completely different, the fractional order models of Eq. (8) are generally non-identical (disproportionate) order systems; Otherwise, each fractional order is an integer multiple of the base order( is order factor),…”

Section: Description Of Nonlinear Fractional Order Modelmentioning

confidence: 99%

“…More and more researchers began to pay attention to fractional models, and found that fractional model has more accurate description method for many physical processes [5,6]. In order to deal with the modeling problems of fractional order system, some modeling methods are presented to deal with parameters identification and fractional orders estimation, including poisson moment functions (PMF) [7,8], modulation functions [9,10], auxiliary variable method [11], orthogonal basis functions [12], and block pulse functions [13], etc.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Identification of Fractional Order System with Scarce Measurement Data Based on Multi Innovation Estimation Algorithm

Wang¹,

Qian²,

Qin³

et al. 2021

Preprint

View full text Add to dashboard Cite

Aiming at the modeling issues of fractional order Hammerstein system with scarce measurements, a novel multi-innovation hybrid identification algorithm is proposed to deal with them. Firstly, a multi-innovation estimation algorithm based on auxiliary model is presented to estimate the parameters of the nonlinear fractional order system, and a multi-innovation Levenberg-Marquardt algorithm are derived to confirm the fractional orders. Secondly, the convergence properties of the proposed algorithm are analyzed using the lemmas and theorems. Finally, in order to illustrate the effectiveness of the proposed algorithm, two fractional order nonlinear systems with scarce measurements are studied to prove the validity.

show abstract

Section: Description Of Nonlinear Fractional Order Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Identification of Fractional Order System with Scarce Measurement Data Based on Multi Innovation Estimation Algorithm

Wang¹,

Qian²,

Qin³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…22,23 However, the stochastic gradient (SG) algorithm has a poor convergence rate because it does not make sufficient use of data. By using the multi-innovation identification theory, [24][25][26][27] the data filtering technique, and the maximum likelihood method, many efficient gradient-based methods are developed for online identification 28 and off-line identification. 29,30 For example, Liu et al presented an SG algorithm for multivariate systems and analyzed the convergence properties of the presented algorithm.…”

Section: Introductionmentioning

confidence: 99%

The innovation algorithms for multivariable state‐space models

Ding

Xiao

2019

Adaptive Control & Signal

115

View full text Add to dashboard Cite

This paper derives the input-output representation of the dynamical system described by a linear multivariable state-space model and the corresponding multivariate linear regressive model (ie, multivariate equation-error model). A projection identification algorithm, a multivariate stochastic gradient identification algorithm, and a multi-innovation stochastic gradient (MISG) identification algorithm are proposed for multivariate equation-error systems by using the negative gradient search and the multi-innovation identification theory. The convergence analysis of the MISG algorithm indicates that the parameter estimation errors converge to zero under the persistent excitation condition. Finally, a numerical example illustrates the effectiveness of the proposed algorithms.

show abstract

“…To improve the robustness of the system, we mainly proceed from two aspects, namely, modeling and control schemes. In terms of modeling, as a generalization from traditional calculus, fractional calculus enjoys both conciseness and veracity in complex system modeling, parameter estimation and control . Fractional‐order system (FOS) theory, as well as fractional‐order controller design, has attracted lots attention in recent years.…”

Section: Introductionmentioning

confidence: 99%

Differential flatness‐based ADRC scheme for underactuated fractional‐order systems

Wei

Zhou

et al. 2020

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

This article mainly studies the fractional-order active disturbance rejection control (FOADRC) schemes for the underactuated commensurate fractional-order systems (FOSs). The FOADRC framework for linear FOSs-based fractional proportion integration differentiation is constructed by using the fractional-order tracking differentiator and the fractional-order extended state observer, and the necessary conditions for the system to have stable controllers are provided. The FOADRC scheme for underactuated FOSs based on differential flatness is proposed. For underactuated FOSs, a set of flat output expressions with a fixed format is given under the controllable condition of the system. Moreover, making the flat output as the equivalent of the system output is simple and easy to analyze and calculate. Subsequently, the FOADRC scheme is designed by using the flat output. Finally, the scheme proposed in this article is verified by a simulation example.

show abstract

An innovative parameter estimation for fractional-order systems in the presence of outliers

Cited by 36 publications

References 30 publications

Identification of Fractional Order System with Scarce Measurement Data Based on Multi Innovation Estimation Algorithm

Identification of Fractional Order System with Scarce Measurement Data Based on Multi Innovation Estimation Algorithm

The innovation algorithms for multivariable state‐space models

Differential flatness‐based ADRC scheme for underactuated fractional‐order systems

Contact Info

Product

Resources

About