Parameter and differentiation order estimation in fractional models

Victor, Stéphane; Malti, Rachid; Garnier, Hugues; Oustaloup, Alain

doi:10.1016/j.automatica.2013.01.026

Cited by 204 publications

(67 citation statements)

References 47 publications

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“…Furthermore, generalization of some results of rational (or integer-) order systems should be done with a lot of care. There are many areas of development of fractional order tools in modeling, system identification and control system design, [34,58,24]. Moreover, it would be particularly interesting for the researchers to apply their theoretical developments on real technological and/or industrial problems.…”

Section: ) How Can Fractional Models Based On Nonsingular and Non-locmentioning

confidence: 99%

Fractional Calculus: D’où Venons-Nous? Que Sommes-Nous? Où Allons-Nous?

Machado

Mainardi

Kiryakova

et al. 2016

FCAA

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Section: ) How Can Fractional Models Based On Nonsingular and Non-locmentioning

confidence: 99%

Fractional Calculus: D’où Venons-Nous? Que Sommes-Nous? Où Allons-Nous?

Machado

Mainardi

Kiryakova

et al. 2016

FCAA

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“…The algorithm should produce accurate estimates by filtering the data and using an iterative technique such as the algorithm srivcf proposed by Victor et al (2013). Finally, Eqn.…”

Section: Remarkmentioning

confidence: 99%

“…In this case, the simplified refined instrumental variable for the continuous-time fractional models (srivcf) algorithm is used because it is known to produce accurate estimates (Victor et al, 2013). Using Eqn.…”

Section: 1mentioning

confidence: 99%

“…A number of results are available for parameter estimation, mainly using different conventional approaches. For details, the reader can refer to the works of Narang et al (2011), Victor et al (2013) and Yakoub et al (2015), and the references therein. The conventional approaches are relevant when a priori knowledge of statistical assumptions about measurement noises is available.…”

Section: Introductionmentioning

confidence: 99%

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Recursive set membership estimation for output–error fractional models with unknown–but–bounded errors

Amairi

2016

International Journal of Applied Mathematics and Computer Science

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This paper presents a new formulation for set-membership parameter estimation of fractional systems. In such a context, the error between the measured data and the output model is supposed to be unknown but bounded with a priori known bounds. The bounded error is specified over measurement noise, rather than over an equation error, which is mainly motivated by experimental considerations. The proposed approach is based on the optimal bounding ellipsoid algorithm for linear output-error fractional models. A numerical example is presented to show effectiveness and discuss results.

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“…For instance, a fractional version of the extended Kalman filter has been proposed in [4] to estimate the unknown parameters and the fractional differentiation orders of a discrete FOS; a fractional version of Zak-Walcott sliding mode observer is introduced in [5] for the joint estimation of the pseudo-states and the unknown input of FOS. Victor et al [6] associated a simplified refined instrumental variable method with a GaussNewton approach to estimate the unknown parameters and the fractional differentiation orders. Other estimation techniques can be found in [7], [8], [9], [10], and references therein.…”

Section: Introductionmentioning

confidence: 99%

Parameters and fractional differentiation orders estimation for linear continuous-time non-commensurate fractional order systems

Belkhatir

Laleg‐Kirati

2018

Systems & Control Letters

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This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.

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Parameter and differentiation order estimation in fractional models

Cited by 204 publications

References 47 publications

Fractional Calculus: D’où Venons-Nous? Que Sommes-Nous? Où Allons-Nous?

Fractional Calculus: D’où Venons-Nous? Que Sommes-Nous? Où Allons-Nous?

Recursive set membership estimation for output–error fractional models with unknown–but–bounded errors

Parameters and fractional differentiation orders estimation for linear continuous-time non-commensurate fractional order systems

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