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Innovative fractional derivative estimation of the pseudo-state for a class of fractional order linear systems

AUTOMATICA 2019年 99卷 157-166页

作者： Wei, Yan-Qiao Liu, Da-Yan Boutat, Driss Univ Orleans INSA PRISME Ctr Vat LoireEA 4229 F-18022 Bourges France

In this paper, a non-asymptotic and robust method is proposed to estimate the fractional integral and derivative of the pseudo-state for a class of fractional order linear systems in noisy environment with unknown initial conditions. To the best of our knowledge, no method has been developed for such estimation. Firstly, the estimation problem is transformed into estimating the fractional integral and derivative of the output and a set of fractional derivative initial values. Then, algebraic integral formulas are exactly derived for the sought estimators by applying different modulating functions with specified properties. In particular, a design parameter is introduced in the formulas of fractional derivative initial values, which can improve the robustness by choosing appropriate values. Secondly, it is shown how to construct the required modulating functions in an efficient way, where another design parameter is involved. Moreover, some error analysis is given to choose the design parameters. Finally, numerical simulations are provided to demonstrate the efficiency and the robustness to noises of the proposed method. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Non-asymptotic estimation modulating functions method Fractional integral and derivative of pseudo-state Fractional derivative of output Fractional derivative initial values

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

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SYSTEMS & CONTROL LETTERS 2018年 115卷 26-33页

作者： Belkhatir, Zehor Laleg-Kirati, Taous Meriem KAUST Div Comp Elect & Math Sci & Engn CEMSE Thuwal Saudi Arabia

This paper proposes a two steps algorithm for the joint estimation of parameters and 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. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. A potential application of the proposed algorithm consists in estimating the fractional differentiation orders of a fractional neurovascular model along with the neural activity considered as an input for this model. To assess the performance of the proposed method, different numerical tests are conducted. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Linear fractional order systems Non-commensurate orders Parameters and fractional differentiation orders estimation modulating functions method

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Estimation of Multiple Point Sources for Linear Fractional Order Systems Using modulating functions

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IEEE CONTROL SYSTEMS LETTERS 2018年第1期2卷 7-12页

作者： Belkhatir, Zehor Laleg-Kirati, Taous-Meriem King Abdullah Univ Sci & Technol Comp Elect & Math Sci & Engn Div Thuwal 239556900 Saudi Arabia

This letter proposes an estimation algorithm for the characterization of multiple point inputs for linear fractional order systems. First, using polynomial modulating functions method and a suitable change of variables the problem of estimating the locations and the amplitudes of a multi-pointwise input is decoupled into two algebraic systems of equations. The first system is nonlinear and solves for the time locations iteratively, whereas the second system is linear and solves for the input's amplitudes. Second, closed form formulas for both the time location and the amplitude are provided in the particular case of single point input. Finally, numerical examples are given to illustrate the performance of the proposed technique in both noise-free and noisy cases. The joint estimation of pointwise input and fractional differentiation orders is also presented. Furthermore, a discussion on the performance of the proposed algorithm is provided.

关键词： Linear fractional order systems pointwise input estimation modulating functions method

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Robust estimation of the fractional integral and derivative of the pseudo-state for a class of fractional order linear systems 37

Robust estimation of the fractional integral and derivative ...

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37th Chinese Control Conference (CCC)

作者： Wei, Yan-Qiao Liu, Da-Yan Boutat, Driss Liu, Hao-Ran Univ Orleans INSA Ctr Val de Loire PRISMEEA 4229 F-18022 Bourges France Yanshan Univ Sch Informat Sci & Engn Qinhuangdao 066004 Hebei Peoples R China

ISBN: (纸本)9789881563958

This paper aims at non-asymptotically estimating the fractional integral and derivative of the pseudo-state for a class of fractional order linear systems in noisy environment with unknown initial conditions. For this purpose, the estimation problem is transformed to estimate the fractional integral and derivative of the output and a set of unknown initial conditions. Then, the modulating functions method is applied to obtain explicit algebraic integral formulae, which give robust estimations in discrete noisy case. Finally, numerical simulations are provided to demonstrate the efficiency of the proposed method.

关键词： Fractional integral and derivative of pseudo-state Non-asymptotic estimation modulating functions method Initial conditions

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Nonasymptotic Pseudo-State Estimation for a Class of Fractional Order Linear Systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2017年第3期62卷 1150-1164页

作者： Wei, Xing Liu, Da-Yan Boutat, Driss Univ Orleans INSA Ctr Val de Loire F-18020 Bourges France

This paper aims at designing a nonasymptotic and robust pseudo-state estimator for a class of fractional order linear systems which can be transformed into the Brunovsky's observable canonical form of pseudo-state space representation with unknown initial conditions. First, this form is expressed by a fractional order linear differential equation involving the initial values of the fractional sequential derivatives of the output, based on which the modulating functions method is applied. Then, the former initial values and the fractional derivatives of the output are exactly given by algebraic integral formulae using a recursive way, which are used to nonasymptotically estimate the pseudo-state of the system in noisy environment. Second, the pseudo-state estimator is studied in discrete noisy case, which contains the numerical error due to a used numerical integration method, and the noise error contribution due to a class of stochastic processes. Then, the noise error contribution is analyzed, where an error bound useful for the selection of design parameter is provided. Finally, numerical examples illustrate the efficiency of the proposed pseudo-state estimator, where some comparisons with the fractional order Luenberger- like observer and a new fractional order H-infinity-like observer are given.

关键词： Fractional order H-infinity-like observer fractional order linear systems fractional order Luenberger-like observer initial conditions modulating functions method nonasymptotic pseudo-state estimation

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Robust estimation of the fractional integral and derivative of the pseudo-state for a class of fractional order linear systems

Robust estimation of the fractional integral and derivative ...

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第37届中国控制会议

作者： Yan-Qiao Wei Da-Yan Liu Driss Boutat Hao-Ran Liu INSA Centre Val de Loire Université d'Orléans School of Information Science and Engineering Yanshan University

关键词： Fractional integral and derivative of pseudo-state Non-asymptotic estimation modulating functions method Initial conditions

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Robust estimation for the fractional integral and derivative of the output for a class of fractional order linear systems 36

Robust estimation for the fractional integral and derivative...

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第36届中国控制会议

作者： Yan-Qiao Wei Xing Wei Da-Yan Liu Driss Boutat INSA Centre Val de Loire Universite d'Orleans

ISBN: (纸本)9781538629185

This paper aims at non-asymptotically estimating the fractional integral and derivative of the output for a class of fractional order linear systems in noisy environment with unknown initial *** this purpose,the considered system modeled by the pseudo-state space representation is firstly transformed into a fractional order differential ***,based on the obtained equation the modulating functions method is applied to obtain algebraic integral formulae for the desired fractional integral and derivative,where the undesired initial conditions are *** integral formulae can give robust estimations in discrete noisy ***,it is shown how to construct the used modulating ***,numerical simulations are provided to demonstrate the efficiency of the proposed method.

关键词： Fractional integral and derivative estimator pseudo-state space representation non-asymptotic estimation modulating functions method

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An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation

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SIGNAL PROCESSING 2015年 116卷 78-90页

作者： Liu, Da-Yan Tian, Yang Boutat, Driss Laleg-Kirati, Taous-Meriem Univ Orleans INSA Ctr Val Loire PR1SME EA 4229 F-18022 Bourges France Nanjing Univ Sci & Technol Sch Automat Sinofrench Joint Lab Automat & Signal Proc Nanjing Jiangsu Peoples R China KAUST CEMSE Div Thuwal 239556900 Saudi Arabia

This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Fractional order differentiator Riemann-Liouville derivative Algebraic parametric method modulating functions method Unknown input Noise error analysis

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modulating functions BASED ALGORITHM FOR THE ESTIMATION OF THE COEFFICIENTS AND DIFFERENTIATION ORDER FOR A SPACE-FRACTIONAL ADVECTION-DISPERSION EQUATION

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2015年第6期37卷 A2813-A2839页

作者： Aldoghaither, Abeer Liu, Da-Yan Laleg-Kirati, Taous-Meriem KAUST Comp Elect & Math Sci & Engn Div Thuwal 539556900 Saudi Arabia Univ Orleans INSA Ctr Val Loire PRISME EA 4229 Bourges France

In this paper, a new method, based on the so-called modulating functions, is proposed to estimate average velocity, dispersion coefficient, and differentiation order in a space-fractional advection-dispersion equation, where the average velocity and the dispersion coefficient are space-varying. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transformed into a linear system of algebraic equations. Then, the modulating functions method combined with a Newton's iteration algorithm is applied to estimate the coefficients and the differentiation order simultaneously. The local convergence of the proposed method is proved. Numerical results are presented with noisy measurements to show the effectiveness and robustness of the proposed method. It is worth mentioning that this method can be extended to general fractional partial differential equations.

关键词： fractional advection-dispersion equation parameter identification fractional order estimation modulating functions method

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Joint state and parameter estimation for a class of cascade systems: Application to a hemodynamic model 13

Joint state and parameter estimation for a class of cascade ...

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13th European Control Conference (ECC)

作者： Zayane-Aissa, Chadia Liu, Da-Yan Laleg-Kirati, Taous-Meriem King Abdullah Univ Sci & Technol Comp Elect & Math Sci & Engn Div Thuwal Saudi Arabia

ISBN: (纸本)9783952426913

In this paper, we address a special case of state and parameter estimation, where the system can be put on a cascade form allowing to estimate the state components and the set of unknown parameters separately. Inspired by the nonlinear Balloon hemodynamic model for functional Magnetic Resonance Imaging problem, we propose a hierarchical approach. The system is divided into two subsystems in cascade. The state and input are first estimated from a noisy measured signal using an adaptive observer. The obtained input is then used to estimate the parameters of a linear system using the modulating functions method. Some numerical results are presented to illustrate the efficiency of the proposed method.

关键词： Joint state and parameter estimation Adaptive observers modulating functions method Balloon Model fMRI

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