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science China(Information sciences) 2024年第6期67卷 328-341页

作者： Xian-Ming ZHANG Qing-Long HAN Bao-Lin ZHANG Xiaohua GE Dawei ZHANG school of {1. Computingand Engineering TechnologiesSwinburne University of Technology College of Automation and Electronic Engineering Qingdao University of Science & Technology school of {1. Shandong University

This paper is concerned with event-triggered H∞control of sampled-data systems. Its novelties lie in three aspects:（i） A novel accumulated-state-error-based event-triggered scheme is introduced by comparing the integral of the state error from tk to t with the system state sampled at tk. This condition works well due to the fact that the so-called Zeno behaviour does not occur.（ii） A novel Lyapunov functional is constructed to establish a criterion to ensure some certain H∞performance of the closed-loop system. This Lyapunov functional is dependent on the integral of the state error involved in the event-triggered scheme.（iii） Under the event-triggered sampling scheme, suitable state-feedback controllers can be designed rather than be given a priori. Moreover, a self-triggered implementation of the proposed event-triggered sampling scheme is presented as well. Finally, a batch reactor model and an inverted pendulum system are given to demonstrate the effectiveness of the proposed method.

关键词： event-triggered sampling self-triggered implementation H ∞ control looped-functional

Global Solvability for a Predator-Prey Model with Prey-Taxis and Rotational Flux Terms

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Chinese Annals of mathematics,Series B 2024年第2期45卷 297-318页

作者： Guoqiang REN Bin LIU school of {1. and Statistics Huazhong University of Science and Technology Hubei Key Laboratory of Engineering Modeling and Scientific computing Huazhong Universityof Science and Technology

In this paper the author investigates the following predator-prey model with prey-taxis and rotational?ux terms■in a bounded domain with smooth *** presents the global existence of generalized solutions to the model... 详细信息

关键词： Predator-prey Prey-taxis Giopal existence Kotational flnux

New Results on Equivalence of Multivariate Polynomial Matrices

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Journal of Systems science & Complexity 2024年

作者： GUAN Jiancheng LIU Jinwang ZHENG Licui WU Tao LIU Jie school of {1. and computing science Hunan University of science and Technology

This paper investigates equivalence of square multivariate polynomial matrices with the determinant being some power of a univariate irreducible *** authors give a necessary and sufficient condition for this *** the authors present an algorithm to reduce a class of multivariate polynomial matrices to their Smith forms.

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Mean-square exponential stability of stochastic Volterra systems in infinite dimensions

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science China(Information sciences) 2024年第10期67卷 298-314页

作者： Lin FU Shiguo PENG Feiqi DENG Quanxin ZHU school of Automation Guangdong University of Technology school of Automation {1. and Engineering South China University of Technology Key Laboratory of computing and Stochastic {1.(Ministry of Education) School of Mathematics and StatisticsHunan Normal University

Over the past decade, the study of stability theory in integro-differential systems has grown significantly owing to their relevance in solving physical and engineering problems, such as viscoelasticity and thermo-viscoelasticity in materials with memory properties. This paper concentrates on a class of infinite-dimensional stochastic integro-differential systems. We establish the well-posedness of the system and identify mild solutions to the system and an abstract stochastic Cauchy problem. This identification is identified by employing a semigroup approach combined with Yosida approximation. We derive sufficient conditions that ensure the mean-square exponential stability of mild solutions to the system boils down to the boundedness of a certain function and a norm estimate for the stochastic part. These conditions are implemented through the semigroup approach and the composition operator method. Illustrative examples are provided and the obtained theoretical results are validated by numerical simulations.

关键词： stochastic integro-differential equations mean-square exponential stability stochastic distributed parameter systems Hardy space composition operators

MULTIFRACTAL ANALYSIS OF CONVERGENCE EXPONENTS FOR PRODUCTS OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS

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Acta Mathematica Scientia 2024年第4期44卷 1594-1608页

作者： Lulu FANG Jihua MA Kunkun SONG Xin YANG school of {1. and Statistics Nanjing University of Science and TechnologyNanjing210094China school of {1. and Statistics Wuhan UniversityWuhan 430072China Key Laboratory of computing and Stochastic {1.(Ministry of Education) School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China

For each real number x∈(0,1.,let[a_(1.(x),a_(2)(x),…,a_n(x),…]denote its continued fraction *** study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1.a_(n)(x)a_(n+1.(x))^(-s)<∞},which reflects the growth rate of the product of two consecutive partial *** a main result,the Hausdorff dimensions of the level sets ofτ(x)are determined.

关键词： continued fractions product of partial quotients Hausdorff dimension

A TRUST-REGION METHOD FOR SOLVING TRUNCATED COMPLEX SINGULAR VALUE DECOMPOSITION

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Journal of Computational mathematics 2024年第4期42卷 999-1031页

作者： Jiaofen Li Lingchang Kong Xuefeng Duan Xuelin Zhou Qilun Luo school of {1. and computing science Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuangxi Key Laboratory of Automatic Detecting Technology and InstrumentsGuilin University of Electronic TechnologyCenter for Applied Mathematics of Guangxi(GUET)Guilin 541004China school of Mathematical {1.s South China Normal UniversityGuangzhou 510000China school of {1. and computing science Guilin University of Electronic TechnologyGuilin 541004China school of {1. and computing science Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuilin University of Electronic TechnologyCenter for Applied Mathematics of Guangxi(GUET)Guilin 541004China school of {1. and Statistics Yunan UniversityKunming 650000China

The truncated singular value decomposition has been widely used in many areas of science including engineering,and statistics,*** this paper,the original truncated complex singular value decomposition problem is formulated as a Riemannian optimiza-tion problem on a product of two complex Stiefel manifolds,a practical algorithm based on the generic Riemannian trust-region method of Absil et *** presented to solve the underlying problem,which enjoys the global convergence and local superlinear conver-gence *** experiments are provided to illustrate the efficiency of the proposed *** with some classical Riemannian gradient-type methods,the existing Riemannian version of limited-memory BFGS algorithms in the MATLAB toolbox Manopt and the Riemannian manifold optimization library ROPTLIB,and some latest infeasible methods for solving manifold optimization problems,are also provided to show the merits of the proposed approach.

关键词： Truncated singular value decomposition Riemannian optimization Trust-region method

SHARP POINTWISE-IN-TIME ERROR ESTIMATE OF L1.SCHEME FOR NONLINEAR SUBDIFFUSION EQUATIONS

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Journal of Computational mathematics 2024年第3期42卷 662-678页

作者： Dongfang Li Hongyu Qin Jiwei Zhang school of {1. and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific computing Huazhong University of Science and TechnologyWuhan 430074China school of {1. and Statistics Wuhan UniversityWuhan 430072China

An essential feature of the subdiffusion equations with theα-order time fractional derivative is the weak singularity at the initial *** weak regularity of the solution is usually characterized by a regularity parameterσ∈(0,1.∪(1.2).Under this general regularity assumption,we present a rigorous analysis for the truncation errors and develop a new tool to obtain the stability results,i.e.,a refined discrete fractional-type Grönwall inequality(DFGI).After that,we obtain the pointwise-in-time error estimate of the widely used L1.scheme for nonlinear subdiffusion *** present results fill the gap on some interesting convergence results of L1.scheme onσ∈(0,α)∪(α,1.∪(1.2].Numerical experiments are provided to demonstrate the effectiveness of our theoretical analysis.

关键词： Sharp pointwise-in-time error estimate Ll scheme Nonlinear subdiffusion equations Non-smooth solutions

A Deep Learning Method for computing Eigenvalues of the Fractional Schrödinger Operator

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Journal of Systems science & Complexity 2024年第2期37卷 391-412页

作者： GUO Yixiao MING Pingbing LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of Mathematical {1.s University of Chinese Academy of SciencesBeijing 100049China

The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger *** proposed approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior knowledge of the *** improvements enable the proposed method to handle both high-dimensional problems and problems posed on irregular bounded *** authors successfully compute up to the first 30 eigenvalues for various fractional Schrödinger *** an application,the authors share a conjecture to the fractional order isospectral problem that has not yet been studied.

关键词： Eigenvalue problem deep learning fractional Schrödinger operator isospectral problem

Reinforcement Learning-Empowered Graph Convolutional Network Framework for Data Integrity Attack Detection in Cyber-Physical Systems

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CSEE Journal of Power and Energy Systems 2024年第2期10卷 797-806页

作者： Edeh Vincent Mehdi Korki Mehdi Seyedmahmoudian Alex Stojcevski Saad Mekhilef school of {1. Computingand Engineering TechnologiesSwinburne University of TechnologyMelbourneAustralia

The massive integration of communication and information technology with the large-scale power grid has enhanced the efficiency, safety, and economical operation of cyber-physical systems. However, the open and diversified communication environment of the smart grid is exposed to cyber-attacks. Data integrity attacks that can bypass conventional security techniques have been considered critical threats to the operation of the grid. Current detection techniques cannot learn the dynamic and heterogeneous characteristics of the smart grid and are unable to deal with non-euclidean data types. To address the issue, we propose a novel Deep-Q-Network scheme empowered with a graph convolutional network (GCN) framework to detect data integrity attacks in cyber-physical systems. The simulation results show that the proposed framework is scalable and achieves higher detection accuracy, unlike other benchmark techniques.

关键词： Deep reinforcement learning graph convolutional network heterogeneous smart grid network

A Pair of Pseudo-differential Operators Involving Index Whittaker Transform in L_(2)^(a) (R_(+);m_(a)(x)dx)

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1420-1430页

作者： Jeetendrasingh MAAN Akhilesh PRASAD Department of mathematics and {1. Indian Institute of Technology(Indian School of Mines)Dhanbad-826004India

Pseudo-differential operators(PDO)Q(x,L_(a,x))and Q(x,L_(a,x))involving the index Whittaker transform are *** for these operators in Hilbert space L_(2)^(a)(R+;m_(a)(x)dx)are obtained.A symbol classΩis *** product an... 详细信息

关键词： Pseudo-differential operator index Whittaker transform confluent hypergeometric functions Hilbert space