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A Decentralized Framework for Kernel PCA With Projection Consensus Constraints

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2025年第5期47卷 3908-3921页

作者： He, Fan Yang, Ruikai Shi, Lei Huang, Xiaolin Shanghai Jiao Tong Univ Inst Image Proc & Pattern Recognit MOE Key Lab Syst Control & Informat Proc Shanghai 200240 Peoples R China Fudan Univ Sch Math Sci Shanghai Key Lab Contemporary Appl Math Shanghai 200240 Peoples R China

This paper studies kernel PCA in a decentralized setting, where data are distributively observed with full features in local nodes, and a fusion center is prohibited. Compared with linear PCA, the use of kernel brings challenges to the design of decentralized consensus optimization: the local projection directions are data-dependent. As a result, the consensus constraint in distributed linear PCA is no longer valid. To overcome this problem, we propose a projection consensus constraint and obtain an effective decentralized consensus framework, where local solutions are expected to be the projection of the global solution on the column space of the local dataset. We also derive a fully non-parametric, fast, and convergent algorithm based on the alternative direction method of multiplier, of which each iteration is analytic and communication-efficient. Experiments on a truly parallel architecture are conducted on real-world data, showing that the proposed decentralized algorithm is effective in utilizing information from other nodes and takes great advantages in running time over the central kernel PCA.

关键词： Principal component analysis Kernel Covariance matrices Vectors Optimization Support vector machines Parallel architectures eigenvalues and eigenfunctions Costs Toy manufacturing industry Kernel methods principal component analysis consensus optimization distributed dataset decentralized algorithms

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Semisupervised Kernel Independent Component Analysis and Its Application for Fault Diagnosis

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2025年 74卷

作者： Kong, Xiangyu Liu, Meizhi Zhang, Qi Luo, Jiayu Zhang, Chen High Tech Inst Xian Xian 710025 Peoples R China Shanxi Datong Univ Coll Phys & Elect Sci Datong 037009 Peoples R China

Fault reconstruction, a common approach for fault diagnosis, involves extracting fault subspaces from measurement data and using them to identify the type of online fault samples. These subspaces, however, are often challenged by insufficient fault representation and weak discriminability among different fault types. To address these issues, a semisupervised kernel independent component analysis (SsKICA) algorithm is proposed and applied in fault diagnosis. First, an innovative feature extraction method is developed that considers both the non-Gaussianity and discriminability of the features in parallel. Its objective function is reformulated into a dual-maximization criterion function that incorporates the supervised information of sample categories and independence into the same mathematical frame. Second, Newton's methods and fixed-point iteration are employed to derive iterative solutions for this dual-maximization function, and the convergence of these iterative solutions is analyzed. Third, a fine-grained fault subspace extraction method is investigated by extending fault reconstruction to the Hilbert space. Finally, a complete fault diagnosis strategy based on SsKICA is designed that can provide feedback for unseen faults and easily interpretable diagnostics. The simulation results, on the Tennessee Eastman process (TEP) and the PROcess Networks Optimization (PRONTO), demonstrate that the proposed method provides effective feedback mechanisms for unseen faults and enhanced diagnostic accuracy for known faults.

关键词： Feature extraction Fault diagnosis Kernel Libraries Data mining Accuracy Principal component analysis eigenvalues and eigenfunctions Training Optimization fault subspace discriminability feature extraction Hilbert space kernel independent component analysis (ICA)

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An Online System Identification Algorithm for Spherical Robot Using the Koopman Theory

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IEEE ROBOTICS AND AUTOMATION LETTERS 2025年第5期10卷 4644-4651页

作者： Guan, Xiaoqing Wang, You Kang, Xiaomeng Yao, Wei Zhang, Jin Li, Guang Zhejiang Univ Inst Cyber Syst & Control State Key Lab Ind Control Technol Hangzhou 310027 Peoples R China Beijing Daxing Int Airport Beijing 102604 Peoples R China Changsha Univ Sci & Technol Sch Comp & Commun Engn Changsha 410114 Peoples R China

This letter proposes a novel linear online identification framework for the spherical robot to address the modeling difficulties posed by nonlinearity and time-varying characteristics. Firstly, the Koopman theory is applied to the spherical robot to build a linear model to approximate the nonlinearity. After selecting a set of observables based on spherical robots' dynamics, the model is identified from data. Then, a new online system identification algorithm based on the Kalman filter and noise estimation was presented, which updates the model in real time to track the time-varying system characteristics. Experiments demonstrate that the Koopman-based linear model meets the precision criteria for long-term forecasting of the nonlinear spherical robot. Through the Kalman filter online identification algorithm, the model parameters can achieve stable convergence, accurately tracking the system changes caused by elements like terrain, load, and actuators. The performance, robustness, and application potential of our algorithm significantly exceed those of traditional methods. After providing a foundation for the spherical robot's adaptive control, this study is also a useful reference for other robots' and nonlinear systems' online identification.

关键词： Robots System identification Adaptation models Load modeling Heuristic algorithms Real-time systems Predictive models Noise eigenvalues and eigenfunctions Online system identification the Kalman filter the Koopman theory the spherical robot time-varying system time-varying system

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Large Array Antenna Spectrum Sensing in Cognitive Radio Networks

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IEEE TRANSACTIONS ON COGNITIVE COMMUNICATIONS AND NETWORKING 2025年第2期11卷 1119-1132页

作者： Taherpour, Amirhossein Taherpour, Abbas Khattab, Tamer Wang, Xiaodong Columbia Univ Dept EE New York NY 10027 USA Imam Khomeini Int Univ Dept EE Qazvin *** Iran Qatar Univ Dept EE Doha Qatar

We investigate spectrum sensing in cognitive radios with large antenna arrays. Gigantic MIMO and extra-large array antennas are fundamental technologies in 5G and future 6G networks, as well as other wireless networks like Wi-Fi. In conventional multiple antenna spectrum sensing, the likelihood ratio test is standard when samples outnumber antennas. It relies on covariance matrix estimates from the sample covariance matrix and its eigenvalues. However, in large array contexts where the number of antennas matches or exceeds the number of samples, the likelihood ratio test falters due to challenges in accurately estimating the covariance matrix from the sample covariance matrix. To address this limitation, we propose and derive three detectors based on linear spectral statistics from random matrix theory: the generalized likelihood ratio, Frobenius norm, and Rao tests, similar to conventional multiple antenna spectrum sensing. We compute the Gaussian distribution of these detectors under the noise-only hypothesis using the central limit theorem for high-dimensional random matrices. Performance evaluation examines how antenna and sample numbers influence outcomes, as confirmed by simulation outcomes. Our results illustrate the effectiveness of the proposed detectors in various real-world situations, encompassing correlated or uncalibrated antennas in networks featuring large array antennas. These detectors exhibit notable benefits, including decreased average signal-to-noise ratio and enhanced detection probability. Their versatility extends to multiple domains, including gigantic MIMO wireless communications, radar systems, and astronomical observations.

关键词： Antenna arrays Covariance matrices Antennas Detectors Sensors eigenvalues and eigenfunctions Wireless networks Cognitive radio spectrum sensing 6G wireless networks large array antenna massive MIMO random matrix theory central limit theorem

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In-plane free vibration analysis of an inclined taut cable with a point mass

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ACTA MECHANICA 2025年第5期236卷 3001-3020页

作者： Patreider, Moritz Wenin, Markus Adam, Christoph Furtmueller, Thomas Univ Innsbruck Unit Appl Mech Technikerstr 13 A-6020 Innsbruck Austria CPE Computat Phys & Engn Weingartnerstr 28 I-39011 Lana Italy

An analytical theory for predicting the free in-plane vibrations of an inclined taut cable carrying a point mass is presented in this paper. A linearized eigenvalue formulation of the problem is derived. It is based on the nonlinear equations of motion and the quasi-static stretching assumption, which assumes that the dynamic tension is piecewise constant to the left and right of the point mass. By neglecting the equation of motion for the longitudinal vibrations in favor of the constitutive cable equation, the equation governing the lateral vibrations can be solved using its boundary conditions. Two coupled linear equations, whose non-trivial solution gives the natural frequencies of the system, can be constructed from the jump and continuity conditions in the longitudinal direction. The comparison of the results with those of a known Galerkin procedure shows that the analytical theory is sufficiently accurate in the applicable parameter range. These results reproduce the curve-veering and the elastic mode transition phenomena known from previous studies. As such, the theory presented here extends the range of applicability of previous analytical cable theories to include inclined cables with point masses as well.

关键词： eigenvalues and eigenfunctions

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Intermittent VIO-Assisted LiDAR SLAM Against Degeneracy: Recognition and Mitigation

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2025年 74卷

作者： Xu, Jiahao Li, Tuan Wang, Hongxia Wang, Zhipeng Bai, Tong Hou, Xiaopeng Beihang Univ Sch Elect & Informat Engn Beijing 100191 Peoples R China CNS ATM State Key Lab Beijing 100191 Peoples R China Beijing Inst Technol Adv Res Inst Multidisciplinary Sci Beijing 100081 Peoples R China Beihang Univ Engn Practice & Innovat Ctr Beijing 100191 Peoples R China Beihang Univ Sch Cyber Sci & Technol Beijing 100191 Peoples R China

Light detection and ranging (LiDAR) simultaneous localization and mapping (SLAM) is widely used in intelligent vehicles for environment perception, self-localization, and mapping. However, in specific environments such as long corridors, highways, or caves, LiDAR SLAM may fail to perceive changes in the surrounding environment, leading to an inability to estimate motion, known as LiDAR degeneracy. LiDAR degeneracy significantly affects the accuracy of LiDAR localization. To address this issue, this article proposes a LiDAR degeneracy recognition algorithm based on a dynamic threshold and mitigates LiDAR degeneracy by introducing intermittent visual-inertial odometry (VIO). We model dynamic thresholds from position accuracy demands through simple mathematical derivations, avoiding heuristic tuning. We also propose an intermittent VIO that operates only during LiDAR degeneracy, achieving comparable or better position performance with minimal computational resource utilization. To improve the intermittent VIO, we use LiDAR for fast initialization of the VIO and visual feature depth association, and we also introduce LiDAR points as features in VIO motion estimation. Through experiments on simulated and public datasets, our method accurately identifies LiDAR degeneracy and effectively mitigates it. Experimental results show that our method outperforms state-of-the-art methods with lower average CPU usage while achieving similar or higher accuracy.

关键词： Laser radar Accuracy Simultaneous localization and mapping Odometry Location awareness eigenvalues and eigenfunctions Heuristic algorithms Feature extraction Degradation Vehicle dynamics Dynamic threshold LiDAR simultaneous localization and mapping (SLAM) light detection and ranging (LiDAR) degeneracy multisensor fusion visual-inertial odometry (VIO)

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Data-Driven Control of Linear Parabolic Systems Using Koopman Eigenstructure Assignment

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2025年第1期70卷 665-672页

作者： Deutscher, Joachim Ulm Univ Inst Measurement Control & Microtechnol D-89081 Ulm Germany

This article considers the data-driven stabilization of linear boundary controlled parabolic PDEs by making use of the Koopman operator. For this, a Koopman eigenstructure assignment problem is solved, which amounts to determining a feedback of the Koopman open-loop eigenfunctionals assigning a desired finite set of closed-loop Koopman eigenvalues and eigenfunctionals to the closed-loop system. It is shown that the designed controller only needs a finite number of open-loop Koopman eigenvalues and modes of the state. They are determined by extending the classical Krylov-dynamic mode decomposition (DMD) to parabolic systems. For this, only a finite number of pointlike outputs and their temporal samples, as well as temporal samples of the inputs, are required, resulting in a data-driven solution to the eigenstructure assignment problem. Exponential stability of the closed-loop system in the presence of small Krylov-DMD errors is verified. An unstable diffusion-reaction system demonstrates the new data-driven controller design technique for distributed-parameter systems.

关键词： eigenvalues and eigenfunctions Generators Closed loop systems State feedback Aerospace electronics Systematics Spectral analysis Data-driven control Koopman operator modal approach parabolic systems state feedback

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Body resonances for classical waves

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ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 2025年第1期76卷 1-15页

作者： Mantile, Andrea Posilicano, Andrea CNRS Lab Math Reims BP 1039UMR9008 Moulin Housse F-51687 Reims France Univ Reims Moulin Housse BP 1039 F-51687 Reims France Univ Insubria Sez Matemat DiSAT Via Valleggio 11 I-22100 Como Italy

We provide a detailed study of the spectral properties of the linear operator H(epsilon)=-(epsilon 2 chi Omega epsilon+chi Omega epsilon c)Delta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H(\varepsilon )=-(\varepsilon <^>{2}\chi _{\Omega _{\varepsilon }}+\chi _{\Omega <^>{c}_{\varepsilon }})\Delta $$\end{document} modeling, through the wave equation (partial derivative tt+H(epsilon))u=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\partial _{tt}+H(\varepsilon ))u=0$$\end{document}, the dynamics of acoustic waves in the presence of a small inhomogeneity of size epsilon\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon $$\end{document} having high contrast epsilon-2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon <^>{-2}$$\end{document}. In particular, we give precise results on the localization of the resonances of H(epsilon)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H(\varepsilon )$$\end{document} and their first-order epsilon\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \us

关键词： eigenvalues and eigenfunctions

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Stability analyses of micropolar fluid-saturated horizontal porous layer due to the influence of uniform internal heat source and vertical throughflow

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PHYSICS OF FLUIDS 2025年第2期37卷

作者： Barman, Pankaj Natl Inst Technol Warangal Dept Math Hanamkonda 506004 Telangana India

The current article aims to investigate the stability analyses of double-diffusive convection in a horizontal porous layer filled with micropolar fluid due to the influence of a uniform internal heat source and vertical throughflow. The usual normal mode technique is applied to investigate the linear stability analysis, whereas the well-known energy approach is utilized to study the nonlinear stability analysis. The resulting eigenvalue problems corresponding to linear and nonlinear stability theories are numerically solved by employing the bvp4c routine in MATLAB 2024(a). The critical thermal Rayleigh number for both the linear and nonlinear theories are computed for the different values of the flow-regulating parameters and depicted graphically. It is observed that the flow configuration shows stabilizing behavior for upward throughflow but destabilizing behavior for downward throughflow in the presence of an internal heat source.

关键词： eigenvalues and eigenfunctions

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Observer-Based Aperiodic Time-Triggered Intermittent Control for Exponential Consensus of Multi-Agent Systems

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IEEE ACCESS 2025年 13卷 22842-22854页

作者： Xu, Xueming Wang, Qingzhi Fu, Baozeng Wang, Lijie Qingdao Univ Inst Complex Sci Sch Automat Qingdao 266071 Peoples R China Shandong Key Lab Ind Control Technol Qingdao 266071 Peoples R China Liaocheng Univ Sch Math Sci Liaocheng 252000 Peoples R China

In this paper, an observer-based aperiodic time-triggered intermittent control protocol (OATICP) is explored for achieving exponential consensus of multi-agent systems (MASs). The mathematical expression of OATICP is initially put forward. OATICP only relies on the output information at sampling instants to estimate the state of the agent itself, and the state estimation information of the neighbor agents at sampling instants to generate the control signal. Then, for the exponential consensus of MASs under OATICP, the mixed Lyapunov functional (MLF) is constructed to establish sufficient conditions. Thirdly, by resorting to linear matrix inequality (LMI) and singular value decomposition (SVD) techniques, OATICP can be designed to realize the exponential consensus of MASs. As a result, a corollary is obtained. Finally, two simulation examples are provided for verification.

关键词： Protocols Multi-agent systems Symmetric matrices Observers Laplace equations eigenvalues and eigenfunctions Control systems Aerospace electronics Topology Switches Exponential consensus mixed Lyapunov functional multi-agent systems observer-based aperiodic time-triggered intermittent control protocol

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