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

Abstract 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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Recursive set-membership parameter estimation of fractional systems using orthotopic approach

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331217744853 ◽

2018 ◽

Vol 40 (15) ◽

pp. 4185-4197 ◽

Cited By ~ 1

Author(s):

Saif Eddine Hamdi ◽

Messaoud Amairi ◽

Mohamed Aoun

Keyword(s):

Parameter Estimation ◽

System Parameter ◽

A Priori ◽

Fractional Order Systems ◽

Fractional Systems ◽

Order Estimation ◽

Set Membership ◽

Equation Error ◽

Bounded Error ◽

Fractional System

In this paper, set-membership parameter estimation of linear fractional-order systems is addressed for the case of unknown-but-bounded equation error. In such bounded-error context with a-priori known noise bounds, the main goal is to characterize the set of all feasible parameters. This characterization is performed using an orthotopic strategy adapted for fractional system parameter estimation. In the case of a fractional commensurate system, an iterative algorithm is proposed to deal with commensurate-order estimation. The performances of the proposed algorithm are illustrated by a numerical example via a Monte Carlo simulation.

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Advances in System Identification Using Fractional Models

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.2833910 ◽

2008 ◽

Vol 3 (2) ◽

Cited By ~ 71

Author(s):

Rachid Malti ◽

Stephane Victor ◽

Alain Oustaloup

Keyword(s):

System Identification ◽

Least Squares ◽

Prior Knowledge ◽

Time Domain ◽

Simultaneous Estimation ◽

Thermal System ◽

Fractional Model ◽

Output Error ◽

Equation Error ◽

Fractional Models

This paper presents an up to date advances in time-domain system identification using fractional models. Both equation-error- and output-error-based models are detailed. In the former models, prior knowledge is generally used to fix differentiation orders; model coefficients are estimated using least squares. The latter models allow simultaneous estimation of model coefficients and differentiation orders using nonlinear programing. As an example, a thermal system is identified using a fractional model and is compared to a rational one.

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Convergence analysis of a combined output error-equation error algorithm

10.1109/mwscas.1989.101995 ◽

2003 ◽

Cited By ~ 1

Author(s):

J.B. Kenney ◽

C.E. Rohrs

Keyword(s):

Convergence Analysis ◽

Error Equation ◽

Output Error ◽

Equation Error

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Set membership estimation of fractional models in the frequency domain

IFAC Proceedings Volumes ◽

10.3182/20080706-5-kr-1001.00686 ◽

2008 ◽

Vol 41 (2) ◽

pp. 4078-4083 ◽

Cited By ~ 1

Author(s):

F. Khemane ◽

R. Malti ◽

M. Thomassin ◽

T. Raïssi

Keyword(s):

Frequency Domain ◽

Set Membership ◽

Fractional Models

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Output error MISO system identification using fractional models

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2021-0067 ◽

2021 ◽

Vol 24 (5) ◽

pp. 1601-1618

Author(s):

Abir Mayoufi ◽

Stéphane Victor ◽

Manel Chetoui ◽

Rachid Malti ◽

Mohamed Aoun

Keyword(s):

System Identification ◽

Optimization Algorithm ◽

Simulation Analysis ◽

Good Efficiency ◽

Output Error ◽

Single Output ◽

Multiple Input ◽

Fractional Models ◽

Definition Of ◽

Initialization Procedure

Abstract This paper deals with system identification for continuous-time multiple-input single-output (MISO) fractional differentiation models. An output error optimization algorithm is proposed for estimating all parameters, namely the coefficients and the differentiation orders. Given the high number of parameters to be estimated, the output error method can converge to a local minimum. Therefore, an initialization procedure is proposed to help the convergence to the optimum by using three variants of the algorithm. Moreover, a new definition of structured-commensurability (or S-commensurability) has been introduced to cope with the differentiation order estimation. First, a global S-commensurate order is estimated for all subsystems. Then, local S-commensurate orders are estimated (one for each subsystem). Finally the S-commensurability constraint being released, all differentiation orders are further adjusted. Estimating a global S-commensurate order greatly reduces the number of parameters and helps initializing the second variant, where local S-commensurate orders are estimated which, in turn, are used as a good initial hit for the last variant. It is known that such an initialization procedure progressively increases the number of parameters and provides good efficiency of the optimization algorithm. Monte Carlo simulation analysis are provided to evaluate the performances of this algorithm.

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A New Generalization of the P1 Non-Conforming FEM to Higher Polynomial Degrees

Computational Methods in Applied Mathematics ◽

10.1515/cmam-2016-0031 ◽

2017 ◽

Vol 17 (1) ◽

pp. 161-185 ◽

Cited By ~ 1

Author(s):

Mira Schedensack

Keyword(s):

Adaptive Algorithm ◽

Numerical Experiments ◽

Convergence Rates ◽

A Priori ◽

Projection Property ◽

Polynomial Degree ◽

Poisson Problem ◽

Optimal Convergence Rates ◽

New Formulation ◽

Three Space

AbstractThis paper generalizes the non-conforming FEM of Crouzeix and Raviart and its fundamental projection property by a novel mixed formulation for the Poisson problem based on the Helmholtz decomposition. The new formulation allows for ansatz spaces of arbitrary polynomial degree and its discretization coincides with the mentioned non-conforming FEM for the lowest polynomial degree. The discretization directly approximates the gradient of the solution instead of the solution itself. Besides the a priori and medius analysis, this paper proves optimal convergence rates for an adaptive algorithm for the new discretization. These are also demonstrated in numerical experiments. Furthermore, this paper focuses on extensions of this new scheme to quadrilateral meshes, mixed FEMs, and three space dimensions.

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