In this paper, the objective is to estimate the pseudo-state of fractional order systems defined by the Caputo fractional derivative from discrete noisy output measurement. For this purpose, an innovative modulating f...
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In this paper, the objective is to estimate the pseudo-state of fractional order systems defined by the Caputo fractional derivative from discrete noisy output measurement. For this purpose, an innovative modulating functions method is proposed, which can provide non-asymptotic estimation within finite -time and is robust against corrupting noises. First, the proposed method is directly applied to the Brunovsky's observable canonical form of the considered system. Then, the initial value of the pseudo -state is exactly expressed by an algebraic integral formula, based on which the pseudo-state is estimated. Second, the properties and construction of the required modulatingfunctions are studied. Furthermore, error analysis is provided in discrete noise cases, which is useful for improving the estimation accuracy. In order to show the advantages of the proposed method, two numerical examples are given, where both rational order and irrational order dynamical systems are considered. After selecting the design parameters using the provided noise error bound, the pseudo-states of considered systems are estimated. The fractional order Luenberger-like observer and the fractional order H infinity-like observer are also applied. Better than the applied fractional order observers, the proposed method can guarantee the convergence speed and robustness at the same time.(c) 2022 ISA. Published by Elsevier Ltd. All rights reserved.
The paper presents an iterative identification method dedicated for industrial processes. The method consists of two steps. In the first step, a MISO system is identified with the modulating functions method to obtain...
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The paper presents an iterative identification method dedicated for industrial processes. The method consists of two steps. In the first step, a MISO system is identified with the modulating functions method to obtain sub-models with a common denominator. In the second step, the obtained subsystems are re-identified. This procedure enables to obtain the set of models with different denominators of the transfer functions. The algorithm was used for on-line identification of a glass conditioning process. Identification window is divided into intervals, in which the models can be updated based on recent process data, with the use of the integral state observer. Results of the performed simulations for the identified models are compared with the historical process data.
Time-delay systems are widely used to model real problems. Most of the works on such systems assume prior knowledge of the delay, which is mostly unknown in real applications. This paper aims to fast and robustly esti...
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Time-delay systems are widely used to model real problems. Most of the works on such systems assume prior knowledge of the delay, which is mostly unknown in real applications. This paper aims to fast and robustly estimate unknown delay, parameters, and output derivatives for a class of linear time-delay systems in noisy environment. First, the classical modulating functions method is combined with the recursive least square algorithm and the Gauss-Newton method to estimate the coefficients and the time-delay, respectively. Second, the generalized modulating functions method is adopted to provide algebraic integral formulas to estimate the output derivatives using the estimated parameters. Finally, numerical simulations are given to demonstrate the efficiency and robustness of the proposed methods.
In this paper, a method based on modulatingfunctions is proposed to estimate the Cerebral Blood Flow (CBF). The problem is written in an input estimation problem for a damped wave equation which is used to model the ...
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In this paper, a method based on modulatingfunctions is proposed to estimate the Cerebral Blood Flow (CBF). The problem is written in an input estimation problem for a damped wave equation which is used to model the spatiotemporal variations of blood mass density. The method is described and its performance is assessed through some numerical simulations. The robustness of the method in presence of noise is also studied. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
作者：
Asiri S.Laleg-Kirati T.-M.Computer
Electrical and Mathematical Science and Engineering Division (CEMSE) King Abdullah University of Science and Technology (KAUST) Thuwal 23955-6900 Saudi Arabia
In this paper, a method based on modulatingfunctions is proposed to estimate the Cerebral Blood Flow (CBF). The problem is written in an input estimation problem for a damped wave equation which is used to model the ...
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This paper aims at extending the modulating functions method to design a non-asymptotic and robust pseudo-state estimator for a class of fractional order linear systems which can be transformed into the Brunovsky'...
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ISBN:
(纸本)9789881563910
This paper aims at extending the modulating functions method to design a non-asymptotic 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 zero initial conditions. For this purpose, the former form is first expressed by a fractional order linear differential equation. Then, by applying the modulating functions method the fractional derivatives of the output are exactly given by algebraic integral formulae using a recursive way, which are used to non-asymptotically estimate the pseudo-state of the system in noisy environment. Finally, numerical examples illustrate the efficiency of the proposed pseudo-state estimator.
This paper aims at extending the modulating functions method to design a non-asymptotic and robust pseudostate estimator for a class of fractional order linear systems which can be transformed into the Brunovsky's...
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ISBN:
(纸本)9781509009107
This paper aims at extending the modulating functions method to design a non-asymptotic and robust pseudostate 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 zero initial conditions. For this purpose, the former form is rst expressed by a fractional order linear differential equation. Then, by applying the modulating functions method the fractional derivatives of the output are exactly given by algebraic integral formulae using a recursive way, which are used to non-asymptotically estimate the pseudo-state of the system in noisy environment. Finally, numerical examples illustrate the ef ciency of the proposed pseudo-state estimator.
This paper aims to design an online algebraic disturbance estimation method for linear systems with noisy state measurements. The motivation is to provide a fast-convergent and robust online disturbance estimation met...
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This paper aims to design an online algebraic disturbance estimation method for linear systems with noisy state measurements. The motivation is to provide a fast-convergent and robust online disturbance estimation method for active anti-disturbance control systems. By constructing a modulatingfunctions vector, a state-based algebraic integral formula is derived for the disturbance of the studied system. Within a discrete noisy environment, the proposed formula can be numerically executed online with respect to a sliding integration window. Meanwhile, the analysis of error effects is also given based on the proposed formula. Finally, simulation examples are provided to illustrate the efficiency of the proposed method for an open-loop system and a closed-loop system, respectively.
This work is devoted to the nonasymptotic and robust fractional derivative estimation of the pseudo-state for a class of fractional-order nonlinear systems with partial unknown terms in noisy environments. In particul...
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This work is devoted to the nonasymptotic and robust fractional derivative estimation of the pseudo-state for a class of fractional-order nonlinear systems with partial unknown terms in noisy environments. In particular, the estimation for the pseudo-state can be obtained by setting the fractional derivative's order to zero. For this purpose, the fractional derivative estimation of the pseudo-state is achieved by estimating both the initial values and the fractional derivatives of the output, thanks to the additive index law of fractional derivatives. The corresponding algorithms are established in terms of integrals by employing the classical and generalized modulating functions methods. Meanwhile, the unknown part is fitted via an innovative sliding window strategy. Moreover, error analysis in discrete noisy cases is discussed. Finally, two numerical examples are presented to verify the correctness of the theoretical results and the noise reduction efficiency.
This paper aims to design a non-asymptotic and robust state estimator applicable both for Caputo fractional linear and nonlinear systems with noisy outputs. For this purpose, a fractional observable canonical form is ...
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This paper aims to design a non-asymptotic and robust state estimator applicable both for Caputo fractional linear and nonlinear systems with noisy outputs. For this purpose, a fractional observable canonical form is considered to show the idea of the proposed method. First, the considered form is transformed by taking a fractional derivative operator. Second, based on the new form, the modulating functions method with the additive index law of fractional derivatives is used to get exact formulas for the sought variables in continuous noise-free case, which only contain the integrals involving the output and the fractional derivative of the input, without producing any source of errors. Moreover, the integral forms can reduce noisy effect as low-pass filters. Hence, fast convergent and robust estimation can be obtained using discrete noisy outputs. After constructing the required modulatingfunctions, two numerical examples are given to demonstrate the advantages of the proposed estimator by comparing with the fractional order Luenberger-like observer. Copyright (C) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0/)
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