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optimal parameter estimation Under Finite Excitation

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2025年

作者： Xing, Yashan Na, Jing Costa-Castello, Ramon Wu, Jiande Chen, Xinkai Kunming Univ Sci & Technol Fac Mech & Elect Engn Yunnan Key Lab Intelligent Control & Applicat Kunming 650500 Peoples R China Univ Poliecn Catalunya UPC Escola Poliecn Super Engn Ind Barcelona ETSEIB Barcelona 08028 Spain Yunnan Univ Yunnan Key Lab Intelligent Syst & Comp Kunming 650500 Peoples R China Shibaura Inst Technol Dept Elect & Informat Syst Saitama 3378570 Japan

Although parameter estimation of continuous-time systems has been studied for decades, the gradient-descent algorithm and its advancements (e.g., least-squares) were all derived to minimize the error between the measured system output and the predictor/observer output, rather than the estimation error (difference between the unknown parameters and their estimates). Hence, the transient convergence response of the estimation error that depends on the manually set learning gains is difficult to analyze. The main contribution of this article is to propose an optimal parameter estimation method, which can directly minimize a cost function of the estimation error to retain the optimal parameter estimation. For this purpose, filter operations and auxiliary variables are used to derive a constructive formulation of estimation error. Then, a cost function of the extracted estimation error is established and minimized to derive a new parameter update law by using the optimality principle. In this framework, a time-varying gain is obtained to handle the effect of regressor and guarantee the exponential convergence under the classical persistent excitation (PE) condition. Moreover, a further tailored parameter update law including a switching term with an excitation increasing mechanism is studied to adapt a weak finite excitation (FE) condition, where both the transient optimal and steady-state exponential convergence can be still retained. Finally, the efficacy of the proposed estimators is verified via numerical simulations and practical experiments on a proton exchange membrane fuel cell system.

关键词： Convergence parameter estimation estimation error Vectors Cost function Prediction algorithms Transient analysis Iron Tuning Switches Exponential convergence finite excitation (FE) fuel cell system optimal parameter estimation

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optimal parameter estimation Method of Internal Solitary Waves in SAR Images and the Cramer-Rao Bound

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 2016年第6期54卷 3143-3150页

作者： Wang, Peng Wang, Xiaoqing Chong, Jinsong Lu, Yilong Chinese Acad Sci Inst Elect Sci & Technol Microwave Imaging Lab Beijing 100190 Peoples R China Univ Chinese Acad Sci Beijing 100190 Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

parameter estimation of internal solitary waves (ISWs) is an important application of oceanic synthetic aperture radar (SAR) images. Several methods have been widely applied for estimating the parameters of ISWs. Most of these methods assume that the ISW signals are corrupted by additive receiver noise. However, the ISW signals in SAR images suffer from both additive (thermal) and multiplicative (speckle) noises. Therefore, the estimation accuracy of previously proposed methods could not reach the Cramer-Rao bound (CRB). This paper proposes an optimal parameter estimation method of ISWs and derives the CRB for parameter estimation of ISWs. The variances of the estimated ISW parameters are shown to reach the CRB. This optimum estimator is validated using ISW SAR signals taken from simulation data and European Remote Sensing 2 (ERS-2) images. The results show that the proposed method is more accurate and effective than other methods. In addition, it should be noted that this optimality could also refer to parameter estimation of other SAR extended targets with an analytical expression.

关键词： Cramer-Rao bound (CRB) internal solitary waves (ISWs) optimal parameter estimation synthetic aperture radar (SAR)

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optimal parameter-estimation FOR BASIC PROBLEMS OF ECONOMIC OPERATION IN ELECTRIC-POWER SYSTEMS

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optimal CONTROL APPLICATIONS & METHODS 1981年第3期2卷 269-287页

作者： ELHAWARY, ME MANSOUR, SY UNIV ALBERTA DEPT ELECT ENGNEDMONTON T6G 2M7ALBERTACANADA

The paper treats the problem of optimal parameter estimation for some basic models commonly used in conjunction with optimal economic operation studies in integrated electric power systems. Three well-known parameter estimation algorithms are considered for this purpose. The weighted least-squares, Gauss-Newton, and Powell's regression algorithms are utilized to obtain optimal parameters for the fuel cost model of thermal generating sources, active power loss model for the electric network, as well as the active-reactive power loss models. Performance comparisons using some test systems show that the Powell's regression results provide satisfactory optimal estimates.

关键词： Electric power systems optimal parameter estimation parameter estimation algorithms

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optimal parameter-estimation UNDER ZERO EXCESS ASSUMPTIONS IN THE BUHLMANN-STRAUB MODEL

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INSURANCE MATHEMATICS & ECONOMICS 1992年第3期11卷 167-171页

作者： DEVYLDER, F GOOVAERTS, M CATHOLIC UNIV LEUVEN B-3000 LOUVAIN BELGIUM UNIV CATHOLIQUE LOUVAIN B-1348 LOUVAIN BELGIUM UNIV AMSTERDAM AMSTERDAM NETHERLANDS

We prove that classical estimators and pseudo-estimators used in the Buhlmann-Straub credibility theory model are optimal, in the sense of minimum variance, under zero excess assumptions on the involved random variables.

关键词： optimal parameter estimation BUHLMANN-STRAUB MODEL

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Cross-validatory framework for optimal parameter estimation of KPCA and KPLS models

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CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 2017年 167卷 196-207页

作者： Fu, Yujia Kruger, Uwe Li, Zhe Xie, Lei Thompson, Jillian Rooney, David Hahn, Juergen Yang, Huizhong Rensselaer Polytech Inst Dept Biomed Engn Troy NY 12180 USA Jiangnan Univ Key Lab Adv Proc Control Light Ind Wuxi 214122 Jiangsu Peoples R China Yangzhou Univ Sch Hydraul Energy & Power Engn Yangzhou 225127 Jiangsu Peoples R China Zhejiang Univ State Key Lab Ind Control Technol Hangzhou 310027 Zhejiang Peoples R China Queens Univ Belfast Sch Chem & Chem Engn Belfast BT9 5AG Antrim North Ireland

This article revisits recently proposed methods to determine the kernel parameter and the number of latent components for identifying kernel principal component analysis (KPCA) and kernel partial least squares (KPLS) models. A detailed analysis shows that existing work is neither optimal nor efficient in determining these important parameters and may lead to erroneous estimates. In addition to that, most methods are not designed to simultaneously estimate both parameters, i.e. they require one parameter to be predetermined. To address these practically important issues, the article introduces a cross-validatory framework to optimally determine both parameters. Application studies to a simulation example and a total of three experimental or industrial data sets confirm that the cross-validatory framework outperforms existing methods and yields optimal estimations for both parameters. In sharp contrast, existing work has the potential to substantially overestimate the number of latent components and to provide inadequate estimates for the kernel parameter.

关键词： Nonlinear models Cross-validatory framework optimal parameter estimation Kernel parameter Number of latent variable sets Combined objective function

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NEW ALGORITHM FOR optimal parameter-estimation WITH LINEAR CONSTRAINTS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1990年第3期66卷 503-513页

作者： SOLIMAN, SA CHRISTENSEN, GS UNIV ALBERTA DEPT ELECT ENGNEDMONTON T6G 2E1ALBERTACANADA

This paper presents a new algorithm for optimal parameter estimation problems with linear constraints. The algorithm developed is based on least absolute-value approximations. The problem is solved first using a least-error-square technique, where we add to the cost function the equality constraints via Lagrange multipliers, to obtain a good estimate for the residuals of the measurements, having gained this information, we choose a number of measurements with the smallest residuals. This number equals the number of parameters to be estimated minus the number of constraints. Using these measurements together with the constraints, we obtain a number of observations equal to the number of parameters to be estimated. By using this technique, we show that there is no need to either iterate or use linear programming to obtain the estimation.

关键词： optimal parameter estimation constrained estimation least absolute value

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Adaptive optimal parameter estimation and Control of Servo Mechanisms: Theory and Experiments

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2021年第1期68卷 598-608页

作者： Wang, Shubo Na, Jing Xing, Yashan Qingdao Univ Sch Automat Qingdao 266071 Peoples R China Kunming Univ Sci & Technol Fac Mech & Elect Engn Kunming 650500 Yunnan Peoples R China CSIC UPC Inst Robot & Informat Ind Barcelona 08028 Spain

Most of classical adaptive laws used in adaptive control have been developed based on the gradient descent algorithm to minimize the control error. Hence, the sluggish convergence of tracking error may affect the online learning, making accurate parameter estimation difficult. The aim of this article is to present a new adaptive law to achieve optimal parameter estimation, and then to showcase its application to adaptive control for a benchmark servo system to retain simultaneous convergence of both the estimation error and tracking error. For this purpose, an auxiliary filter is introduced to extract the estimation error, which is used to drive the adaptive law with a time-varying gain to minimize a cost function of the estimation error to achieve fast, accurate parameter estimation. Finally, this new adaptation is incorporated into an adaptive nonsingular terminal sliding-mode control for the considered servo system to obtain tracking control and parameter estimation simultaneously. The effectiveness of the developed method is validated by means of comparative simulations and experiments.

关键词： Adaptive control optimal parameter estimation servo mechanisms sliding-mode control

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Persistently-exciting signal generation for optimal parameter estimation of constrained nonlinear dynamical systems

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ISA TRANSACTIONS 2018年 77卷 231-241页

作者： Honorio, Leonardo M. Costa, Exuperry Barros Oliveira, Edimar J. Fernandes, Daniel de Almeida Moreira, Antonio Paulo G. M. Univ Fed Juiz de Fora Dept Energy Juiz De Fora Brazil Univ Porto Fac Engn Porto Portugal

This work presents a novel methodology for Sub-optimal Excitation Signal Generation and optimal parameter estimation of constrained nonlinear systems. It is proposed that the evaluation of each signal must also account for the difference between real and estimated system parameters. However, this metric is not directly obtained once the real parameter values are not known. The alternative presented here is to adopt the hypothesis that, if a system can be approximated by a white box model, this model can be used as a benchmark to indicate the impact of a signal over the parametric estimation. In this way, the proposed method uses a dual layer optimization methodology: (i) Inner Level;For a given excitation signal a nonlinear optimization method searches for the optimal set of parameters that minimizes the error between the outputs of the optimized and benchmark models. (ii) At the outer level, a metaheuristic optimization method is responsible for constructing the best excitation signal, considering the fitness coming from the inner level, the quadratic difference between its parameters and the cost related to the time and space required to execute the experiment. (C) 2018 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： optimal signal generation optimal parameter estimation Optimization in parameter estimation Constrained systems parameter estimation optimal Input Design Non-linear systems

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A Convolutional System Identification Approach Mixing optimal parameter estimation and Deep Learning

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INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS 2023年第8期21卷 2674-2684页

作者： Souza, Marina Borges Arantes dos Santos Neto, Accacio F. F. Honorio, Leonardo de Mello de Oliveira, Edimar Jose Silva, Mathaus F. F. Pancoti, Antonio Univ Fed Juiz de Fora Dept Energy Juiz De Fora Brazil

Experimental identification (EI) methods are often discussed in the literature because of the importance of building reliable dynamical models and control systems. This is especially true when thinking about autonomous vehicle control. An important characteristic of EI approaches is the necessity of a signal with good excitation properties to model the system, which is usually obtained by optimal input design approaches. Although this is a method that reproduces the actual behavior through a mathematical tool, it can ignore unmodeled features such as asymmetry or even constructive addictions. In this way, this work aims to construct a hybrid identification method through a mathematical model estimated in convolution with a deep neural network (DNN). The Gated recurrent unit (GRU) must be able to determine the states of the next instant based on the input and output of the theoretical model. The results are promising and suggest that this association is valid and capable of refining the outputs of a purely mathematical model.

关键词： Hybrid identification optimal input design optimal parameter estimation recurrent deep learning

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optimal parameter estimation strategy of PEM fuel cell using gradient-based optimizer

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ENERGY 2022年第PartC期239卷 122096-122096页

作者： Rezk, Hegazy Ferahtia, Seydali Djeroui, Ali Chouder, Aissa Houari, Azeddine Machmoum, Mohamed Abdelkareem, Mohammad Ali Prince Sattam Bin Abdulaziz Univ Coll Engn Wadi Addawaser Al Kharj Saudi Arabia Minia Univ Fac Engn Al Minya Egypt Univ Msila Dept Elect Engn Lab Anal Signaux & Syst Msila Algeria Univ Msila Dept Elect Engn Lab Genie Elect Msila Algeria Univ Nantes Dept Ind Engn IREENA Lab Nantes France Univ Sharjah Dept Sustainable & Renewable Energy Engn POB 27272 Sharjah U Arab Emirates Minia Univ Fac Engn Chem Engn Dept Al Minya Egypt

The exact parameter estimation of the fuel cell model is considered a critical stage in delivering a consistent emulation for the fuel cell system characteristics. The aim of this is to suggeste a robust methodology based on the Gradient-based Optimizer (GBO) to identify the best parameters of PEM fuel cell (PEMFC). Three distinct types of PEM fuel cells: 250 W FC stack, BCS 500 W, and SR-12 500 W, were used to demonstrate the superiority of the GBO. To confirm the superiority of GBO, the results were compared with those obtained using different optimizers such as salp swarm algorithm (SSA), heap-based optimizer (HBO), differential evolution (DE), whale optimization algorithm (WOA), moth-flame optimization algorithm (MFO), sine cosine algorithm (SCA), and Harris's hawk optimizer (HHO). Dur -ing the optimization process, the unknown parameters of PEM fuel cells are used as decision variables, whereas the objective function needs to be minimum is represented by the sum square error between the measured data and estimated data. In addition, the obtained results by GBO are compared with other methods achieved in the literature. The superiority of GBO in determining the optimal parameters of different PEM fuel cells is proved. (c) 2021 Elsevier Ltd. All rights reserved.

关键词： PEM fuel Cell optimal parameter estimation Optimization Energyefficiency Gradient-based optimizer (GBO)

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