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Reduced-order identification methods: Hierarchical algorithm or variable elimination algorithm

AUTOMATICA 2025年 172卷

作者： Chen, Jing Mao, Yawen Wang, Dongqing Gan, Min Zhu, Quanmin Liu, Feng Jiangnan Univ Sch Sci Wuxi 214122 Peoples R China Qingdao Univ Coll Elect Engn Qingdao 266071 Peoples R China Qingdao Univ Coll Comp Sci & Technol Qingdao 266071 Peoples R China Univ West England Dept Engn Design & Math Bristol BS16 1QY England Stevens Inst Technol Sch Syst & Enterprises Hoboken NJ 07030 USA

Reduced-order identification algorithms are usually used in machine learning and big data technologies, where the large-scale systems widely exist. For large-scale system identification, traditional least squares algorithm involves high-order matrix inverse calculation, while traditional gradient descent algorithm has slow convergence rates. The reduced-order algorithm proposed in this paper has some advantages over the previous work: (1) via sequential partitioning of the parameter vector, the calculation of the inverse of a high-order matrix can be reduced to low-order matrix inverse calculations;(2) has a better conditioned information matrix than that of the gradient descent algorithm, thus has faster convergence rates;(3) its convergence rates can be increased by using the Aitken acceleration method, therefore the reduced-order based Aitken algorithm is at least quadratic convergent and has no limitation on the step-size. The properties of the reduced-order algorithm are also given. Simulation results demonstrate the effectiveness of the proposed algorithm. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Reduced-order algorithm Least square algorithm gradient descent algorithm Condition number Hierarchical identification algorithm Variable elimination algorithm

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Distributed optimization algorithm for multi-agent networks with lazy gradient information

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ASIAN JOURNAL OF CONTROL 2025年第1期27卷 532-539页

作者： Mo, Lipo Yang, Yang Huang, Xiankai Beijing Technol & Business Univ Sch Math & Stat Beijing 100048 Peoples R China Beijing Technol & Business Univ Sch Comp & Artificial Intelligence Beijing Peoples R China

Based on the so-called lazy gradient information, this note proposes two communication-reduced distributed optimization algorithms over undirected multi-agent networks. The lazy gradients refer to some gradients that do not change much in the past iterations and thus may not be distributed among agents which correspondingly reduces the communication load in the networks. For both the deterministic and the stochastic frameworks, the asymptotic properties of the distributed optimization algorithms are established. Compared with the existing literature using the lazy gradient information, the proposed algorithms in the paper are fully distributed and more suitable for the situation of decentralized multi-agent networks. The effectiveness of the proposed algorithms is also testified through numerical simulations.

关键词： communication reduction distributed optimization gradient descent algorithm lazy gradient

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A fast LMS-based digital background calibration technique for 16-bit SAR ADC with modified shuffling scheme

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MICROELECTRONICS JOURNAL 2025年 156卷

作者： Wang, Jiacong Du, Biyun Su, Zhangjie Hu, Ke Yu, Jia Cao, Chao Liu, Shubin Guo, Haijun Shandong Univ Sch Integrated Circuits Jinan 250101 Peoples R China Shandong Univ Sch Software Jinan 250101 Peoples R China Xidian Univ Sch Microelect Xian 710071 Peoples R China Univ Jinan Sch Informat Sci & Engn Jinan 250022 Peoples R China

- This paper introduces a modified shuffling scheme to achieve less overhead in ADC, lower power consumption for digital calibration and higher update frequency. Different-size unit capacitors are used in the shuffling, which reduces the number of switches and capacitors by almost half while remaining complexity of the digital circuit unchanged. Additionally, a novel LMS-based digital background calibration technique suitable for split-based ADC is proposed. Fast convergence and linear calibration are achieved with the improved gradient descent algorithm, which uses Momentum and Nesterov accelerated gradient (NAG). The convergence speed is found to be over 10 times faster than typical LMS algorithm and maintain calibration accuracy in MATLAB simulation of a 16-bit, 1 MS/s SAR ADC.

关键词： Split-capacitor SAR ADC Modified shuffling Fast convergency LMS-Based calibration gradient descent algorithm

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Research on three-dimensional attack area based on improved backtracking and ALPS-GP algorithms of air-to-air missile

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Journal of Systems Engineering and Electronics 2025年第1期36卷 292-310页

作者： ZHANG Haodi WANG Yuhui HE Jiale College of Automation Engineering Nanjing University of Aeronautics&AstronauticsNanjing 210016China National Key Laboratory of Air-based Information Perception and Fusion AVICLuoyang 471000China

In the field of calculating the attack area of air-to-air missiles in modern air combat scenarios,the limitations of existing research,including real-time calculation,accuracy efficiency trade-off,and the absence of the three-dimensional attack area model,restrict their practical *** address these issues,an improved backtracking algorithm is proposed to improve calculation efficiency.A significant reduction in solution time and maintenance of accuracy in the three-dimensional attack area are achieved by using the proposed ***,the age-layered population structure genetic programming(ALPS-GP)algorithm is introduced to determine an analytical polynomial model of the three-dimensional attack area,considering real-time *** accuracy of the polynomial model is enhanced through the coefficient correction using an improved gradient descent *** study reveals a remarkable combination of high accuracy and efficient real-time computation,with a mean error of 91.89 m using the analytical polynomial model of the three-dimensional attack area solved in just 10^(-4)s,thus meeting the requirements of real-time combat scenarios.

关键词： air combat three-dimensional attack area improved backtracking algorithm age-layered population structure genetic programming(ALPS-GP) gradient descent algorithm

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Distributed Kernel-Based gradient descent algorithms

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CONSTRUCTIVE APPROXIMATION 2018年第2期47卷 249-276页

作者： Lin, Shao-Bo Zhou, Ding-Xuan Wenzhou Univ Coll Math & Informat Sci Wenzhou Peoples R China City Univ Hong Kong Dept Math Kowloon Hong Kong Peoples R China

We study the generalization ability of distributed learning equipped with a divide-and-conquer approach and gradient descent algorithm in a reproducing kernel Hilbert space (RKHS). Using special spectral features of the gradient descent algorithms and a novel integral operator approach, we provide optimal learning rates of distributed gradient descent algorithms in probability and partly conquer the saturation phenomenon in the literature in the sense that the maximum number of local machines to guarantee the optimal learning rates does not vary if the regularity of the regression function goes beyond a certain quantity. We also find that additional unlabeled data can help relax the restriction on the number of local machines in distributed learning.

关键词： Learning theory Distributed learning gradient descent algorithm Integral operator

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Dynamic Event-Triggered Control for a Class of Uncertain Strict-Feedback Systems via an Improved Adaptive Neural Networks Backstepping Approach

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2025年 22卷 2041-2050页

作者： Xu, Ning Liu, Xiang Li, Yulin Zong, Guangdeng Zhao, Xudong Wang, Huanqing Bohai Univ Coll Informat Sci & Technol Jinzhou 121013 Peoples R China Dongguan Univ Technol Inst Sci & Technol Innovat Dongguan 523000 Peoples R China MIIT Talent Big Data Intelligent Anal & Evaluat Key La Beijing 100804 Peoples R China Nankai Univ Coll Artificial Intelligence Tianjin 300381 Peoples R China Tiangong Univ Sch Control Sci & Engn Tianjin 300387 Peoples R China Bohai Univ Coll Control Sci & Engn Jinzhou 121013 Liaoning Peoples R China Bohai Univ Coll Math Sci Jinzhou 121013 Liaoning Peoples R China

This article focuses on a dynamic event-triggered adaptive neural networks backstepping control for a class of uncertain strict-feedback systems with communication constraints. The uncertain terms including external disturbances and unknown nonlinear functions are approximated by radial basis function neural networks, in which the weight update laws are obtained via the gradient descent algorithm, ensuring the local boundedness of the approximation error of neural networks. Then, to enhance the transmission efficiency of control signals, a dynamic event-triggered mechanism is introduced, which enables the dynamic adjustment of threshold parameters in response to the actual tracking performance. It is strictly proved via the Lyapunov stability criterion that the tracking error can converge to a desired small neighborhood of the origin, and all signals in the closed-loop system are bounded. Finally, the validity of the control strategy is demonstrated through a simulation example. Note to Practitioners-In practical network control systems, control signals are typically transmitted continuously or periodically to devices through the communication network in the form of data packets. As communication networks are usually shared by various system nodes, and resources such as communication channel bandwidth and computational capabilities are limited, improving the transmission efficiency of control signals becomes a crucial design problem for controllers in network control systems. Therefore, This study introduces a control method via event-triggered sampling, aiming to enhance sampling efficiency while ensuring the stability and reliability of the system. The proposed control method is suitable for a broad category of strict-feedback nonlinear systems with communication constraints, offering notable advantages such as low-complexity design and straightforward implementation.

关键词： Adaptation models Adaptive backstepping design strict-feedback systems dynamic event-triggered control gradient descent algorithm neural networks

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Tikhonov regularization and gradient descent algorithms for tomography using first-arrival seismic traveltimes

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CHINESE JOURNAL OF GEOPHYSICS-CHINESE EDITION 2015年第4期58卷 1367-1377页

作者： Cui Yan Wang Yan-Fei Chinese Acad Sci Inst Geol & Geophys Key Lab Petr Resources Res Beijing 100029 Peoples R China China Univ Petr Shengli Coll Dongying 257097 Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China

With the development of seismic exploration, inversion and imaging become key issues because of complex structures. It is in urgent need to build accurate near-surface velocity models. Nowadays, three primary numerical methods are developed to acquire the velocity model, i.e., stack velocity analysis, migration velocity analysis and tomography velocity analysis. For the near-surface seismic problem, the first two methods are not suitable because of insufficient fold numbers and reflections. So the tomography method has received much more attention. First-arrival traveltime seismic tomography refers to inversion of medium velocity using first-arrival seismic wave traveltimes and their ray paths. The first task is model parameterization which discretizes the stratigraphic model into many slowness units by gridding. Secondly, based on the slowness units, the ray paths are analyzed by the shortest traveltime ray tracing. Then the traveltime equation is established to solve the velocity model. This is an ill-posed inverse problem. Proper regularization technique and optimization methods are required. Therefore, a Tikhonov regularization model with constraints on feasible set was established, and a gradient descent method with modified step sizes was also developed to obtain an optimized solution. Three different theoretical models were designed to test the new algorithm. The first is a horizontal layered model: there were three horizontal layers with the velocity of 600 m.s(-1), 1200 m.s(-1) and 2000 m.s(-1) top to bottom in the real model. By random disturbance of the model, we got an initial velocity model which was far away from the real model. The inversion result shows that the new algorithm can converge to the true model quickly even with poor initial condition. This shows that the new algorithm is stable and fast in convergence. Comparison with the well-known conjugate gradient (CG) method indicates that this new algorithm requires less memory and has higher conve

关键词： First-arrival traveltime seismic tomography Regularization gradient descent algorithm Ray tracing

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Distributed gradient descent Localization in Wireless Sensor Networks

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ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2015年第3期40卷 893-899页

作者： Alwan, Nuha A. S. Mahmood, Alaa S. Univ Baghdad Coll Engn Dept Comp Engn Baghdad Iraq

We propose a distributed gradient descent (GD) localization algorithm in 3D space for wireless sensor networks that employ the push-sum (PS) gossip algorithm to compute sums. Sums and averages constitute building blocks for various signal processing applications including the one under consideration. Our contribution lies in combining vector PS and GD approaches achieving fast convergence, high accuracy and a remarkable robustness against link failures. Comparisons are presented with the centralized counterpart and with similar recent works.

关键词： Wireless sensor network Distributed node localization gradient descent algorithm Push-sum gossip algorithm

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gradient descent Bit Flipping algorithms for Decoding LDPC Codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2010年第6期58卷 1610-1614页

作者： Wadayama, Tadashi Nakamura, Keisuke Yagita, Masayuki Funahashi, Yuuki Usami, Shogo Takumi, Ichi Nagoya Inst Technol Nagoya Aichi 4668555 Japan Meijo Univ Nagoya Aichi Japan

A novel class of bit-flipping (BF) algorithm for decoding low-density parity-check (LDPC) codes is presented. The proposed algorithms, which are referred to as gradient descent bit flipping (GDBF) algorithms, can be regarded as simplified gradient descent algorithms. The proposed algorithms exhibit better decoding performance than known BF algorithms, such as the weighted BF algorithm or the modified weighted BF algorithm for several LDPC codes.

关键词： LDPC code bit-flipping algorithm gradient descent algorithm

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On the convergence of gradient descent for robust functional linear regression

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JOURNAL OF COMPLEXITY 2024年 84卷

作者： Wang, Cheng Fan, Jun Huizhou Univ Sch Math & Stat Huizhou Peoples R China Hong Kong Baptist Univ Dept Math Kowloon Hong Kong Peoples R China

Functional data analysis offers a set of statistical methods concerned with extracting insights from intrinsically infinitedimensional data and has attracted considerable amount of attentions in the past few decades. In this paper, we study robust functional linear regression model with a scalar response and a functional predictor in the framework of reproducing kernel Hilbert spaces. A gradient descent algorithm with early stopping is introduced to solve the corresponding empirical risk minimization problem associated with robust loss functions. By appropriately selecting the early stopping rule and the scaling parameter of the robust losses, the convergence of the proposed algorithm is established when the response variable is bounded or satisfies a moment condition. Explicit learning rates with respect to both estimation and prediction error are provided in terms of regularity of the regression function and eigenvalue decay rate of the integral operator induced by the reproducing kernel and covariance function. (c) 2024 Elsevier Inc. All rights reserved.

关键词： Learning theory gradient descent algorithm Robust functional linear regression Learning rate Integral operator

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