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An innovative modulating functions method for pseudo-state estimation of fractional order systems

ISA TRANSACTIONS 2023年 136卷 334-344页

作者： Wang, Jia-Chang Liu, Da-Yan Boutat, Driss Wang, Yong Univ Sci & Technol China Dept Automat Hefei 230026 Peoples R China Univ Orleans INSA PRISME EA 4229 Ctr Val Loire F-18022 Bourges France

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 modulating functions 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.

关键词： modulating functions method Non-asymptotic estimation Fractional order systems Initial value estimation Pseudo-state estimation Error analysis

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Finite-time estimation for a class of systems with unknown time-delay using modulating functions-based method

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ASIAN JOURNAL OF CONTROL 2023年第2期25卷 746-757页

作者： Asiri, Sharefa Liu, Da-Yan King Abdulaziz Univ Dept Math Jeddah Saudi Arabia Univ Orleans INSA Ctr Val Loire Orleans France

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.

关键词： delay estimation derivative estimation modulating functions method parameter estimation

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On-line process identification using the modulating functions method and non-asymptotic state estimation

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ARCHIVES OF CONTROL SCIENCES 2022年第3期32卷 535-555页

作者： Byrski, Witold Drapala, Michal AGH Univ Sci & Technol Dept Automat Control & Robot Al Mickiewicza 30 PL-30059 Krakow Poland

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.

关键词： system identification modulating functions method state observers signal processing adaptive algorithms

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Source Estimation for the Damped Wave Equation Using modulating functions method: Application to the Estimation of the Cerebral Blood Flow

Source Estimation for the Damped Wave Equation Using Modulat...

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20th World Congress of the International-Federation-of-Automatic-Control (IFAC)

作者： Asiri, Sharefa Laleg-Kirati, Taous-Meriem KAUST Comp Elect & Math Sci & Engn Div CEMSE Thuwal 239556900 Saudi Arabia

In this paper, a method based on modulating functions 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.

关键词： Source Estimation Distributed Parameter System Damped Wave Equation Biomedical System modulating functions method Robust Estimation

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Source Estimation for the Damped Wave Equation Using modulating functions method: Application to the Estimation of the Cerebral Blood Flow

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IFAC-PapersOnLine 2017年第1期50卷 7082-7088页

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

关键词： Biomedical System Damped Wave Equation Distributed Parameter System modulating functions method Robust Estimation Source Estimation

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Extension of modulating functions method to pseudo-state estimation for fractional order linear systems 35

Extension of modulating functions method to pseudo-state est...

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35th Chinese Control Conference (CCC)

作者： Wei, Xing Liu, Da-Yan Boutat, Driss Univ Orleans INSA Ctr Val Loire PRISME EA 4229 F-18022 Bourges France

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.

关键词： Fractional order linear systems Non-asymptotic pseudo-state estimation modulating functions method

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Extension of modulating functions method to pseudo-state estimation for fractional order linear systems

Extension of modulating functions method to pseudo-state est...

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第35届中国控制会议

作者： Xing Wei Da-Yan Liu Driss Boutat INSA Centre Val de Loire Universitéd'Orléans PRISME EA 4229

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.

关键词： Fractional order linear systems Non-asymptotic pseudo-state estimation modulating functions method

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Online algebraic disturbance estimation method for linear systems with noisy state measurements

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JOURNAL OF THE FRANKLIN INSTITUTE 2025年第1期362卷

作者： Wei, Yan-Qiao Liu, Da-Yan Hua, Chang-Chun Zhang, Cong Yanshan Univ Sch Elect Engn Qinhuangdao 066004 Hebei Peoples R China Univ Orleans INSA Ctr Val Loire PRISME EA 4229 F-18022 Bourges France

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 modulating functions 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.

关键词： Online algebraic disturbance estimation modulating functions method Disturbed linear system Noisy state measurements

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Nonasymptotic Fractional Derivative Estimation of the Pseudo-State for a Class of Fractional-Order Partial Unknown Nonlinear Systems

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IEEE TRANSACTIONS ON CYBERNETICS 2023年第11期53卷 7392-7405页

作者： Wang, Zhi-Bo Liu, Da-Yan Boutat, Driss Zhang, Xuefeng Shi, Peng Univ Orleans INSA Ctr Val Loire F-18020 Bourges France Northeastern Univ Sch Sci Shenyang 110819 Peoples R China Univ Adelaide Sch Elect & Elect Engn Adelaide SA 5005 Australia

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.

关键词： Estimation Observers Linear systems Noise measurement Convergence Indexes Fractional calculus Fractional derivative estimation fractional-order nonlinear systems initial value estimation modulating functions method nonasymptotic estimation unknown term estimation

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modulating functions based state estimator for Caputo fractional systems 12

Modulating functions based state estimator for Caputo fracti...

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12th IFAC Conference on Fractional Differentiation and its Application (ICFDA)

作者： Liu, Da-Yan Wei, Xing Wei, Yan-Qiao Boutat, Driss Liu, Hao-Ran Univ Orleans INSA Ctr Val Loire PRISME EA4229 F-18020 Bourges France Anyang Inst Technol Sch Elect Informat & Elect Engn Anyang 455000 Peoples R China Yanshan Univ Sch Elect Engn Qinhuangdao 066004 Hebei Peoples R China Yanshan Univ Sch Informat Sci & Engn Qinhuangdao 066004 Hebei Peoples R China

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 modulating functions, 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/)

关键词： Fractional linear systems fractional nonlinear systems non-asymptotic and robust estimation modulating functions method

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