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 ini...
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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 modulatingfunctions 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 modulatingfunctions 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.
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...
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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 modulatingfunctions 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.
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 variable...
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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.
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...
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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.
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...
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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.
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...
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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.
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 consi...
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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.
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 t...
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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.
In this paper, a new method, based on the so-called modulatingfunctions, is proposed to estimate average velocity, dispersion coefficient, and differentiation order in a space-fractional advection-dispersion equation...
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In this paper, a new method, based on the so-called modulatingfunctions, 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.
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. Inspire...
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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.
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