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exponential convergence of Fisher Entropy for Diffusion Processes

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Wuhan University Journal of Natural Sciences 2011年第2期16卷 130-132页

作者： LIU Wei School of Mathematics and Statistics Wuhan UniversityWuhan 430072 Hubei China

In this paper, we introduce the definition of Γ-Fisher entropy. For the stochastic differential equation in Rd and the unique invariant probability measure μ, we obtain the exponential convergence of Γ-Fisher entropy with respect to μ under some condition about Γ and the drift b. Moreover, we revisit the exponential convergence of the usual Fisher entropy under the Bakry Emery condition.

关键词： Fisher entropy diffusion processes exponential convergence

exponential convergence of Finite-dimensional Approximations to Linear Bond-based Peridynamic Boundary Value Problems

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Communications in Mathematical Research 2018年第3期34卷 278-288页

作者： WU HAO Department of Mathematics and Statistics Auburn University

In this paper, we demonstrate that the finite-dimensional approximations to the solutions of a linear bond-based peridynamic boundary value problem converge to the exact solution exponentially with the analyticity ass... 详细信息

关键词： Peridynamics exponential convergence nonlocal boundary value problem analytic function finite-dimensional approximation

Global exponential convergence of Neutral Type Competitive Neural Networks with D Operator and Mixed Delay

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Journal of Systems Science & Complexity 2020年第6期33卷 1785-1803页

作者： AOUITI Chaouki ASSALI El Abed BEN GHARBIA Imen University of Carthage Faculty of Sciences of BizertaDepartment of MathematicsResearch Units of Mathematics and Applications UR13ES477021 ZarzounaBizertaTunisia

The models of competitive neural network(CNN)was in recent past proposed to describe the dynamics of cortical cognitive maps with unsupervised synaptic modifications,where there are two types of memories:Long-term memories(LTM)and short-term memories(STM),LTM presents unsupervised and slow synaptic modifications and STM characterize the fast neural *** paper is concerned with a class of neutral type CNN’s with mixed delay and D *** employing the appropriate differential inequality theory,some sufficient conditions are given to ensure that all solutions of the model converge exponentially to zero ***,an illustrative example is also given at the end of this paper to show the effectiveness of the proposed results.

关键词： Competitive neural networks D operator exponential convergence neutral type delay

exponential convergence of Distributed Optimal Coordination for Linear Multi-Agent Systems over General Digraphs

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Exponential Convergence of Distributed Optimal Coordination ...

Global stabilizer of a general class of feedback nonlinear systems and its exponential convergence

第三十九届中国控制会议

作者： Jin Zhang Lu Liu Haibo Ji Department of Biomedical Engineering City University of Hong Kong University of Science and Technology of China City University of Hong Kong Shenzhen Research Institute

This paper considers the distributed optimal coordination problem of linear multi-agent systems over general directed graphs. By using the left eigenvector associated with the zero eigenvalue of the Laplacian matrix, we propose a new distributed continuous-time control law to ensure all the agent outputs to reach the optimal solution of the global objective function. The exponential convergence of the closed-loop multi-agent system is established when the general directed graph is strongly connected and the local objective functions are strongly convex with locally Lipschitz gradients. Finally, a simulation example is given to validate the effectiveness of the proposed control scheme.

关键词： Optimal coordination linear systems exponential convergence directed graphs

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控制理论与应用（英文版） 2005年第4期3卷 409-414页

作者： Runing MA Jundi DIAN Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing Jiangsu 210016 China

We discuss the global stabilization procedure which renders a general class of feedback nonlinear systems exponential convergent, Our stabilizer consists of a nested saturation function, which is a nonlinear combination of saturation functions. Here we prove the exponential convergence of the stabilizer for the first time and give numerical examples to illustrate the efficiency of the result given above,

关键词： Feedback nonlinear system Saturated control Global stabilization exponential convergence

A FAS approach for stabilization of generalized chained forms: part 1. Discontinuous control laws

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Science China(Information Sciences) 2024年第2期67卷 118-143页

作者： Guang-Ren DUAN Center for Control Theory and Guidance Technology Harbin Institute of Technology Center for Control Science and Technology Southern University of Science and Technology

In this paper, a type of general nonholonomic systems is proposed, which contains both the Brockett’s two example systems, and their extended n-dimensional chained forms, as special cases. For the stabilization of such systems, a stabilizing controller is proposed based on the fully actuated system(FAS)approach, which is discontinuous at the origin but time-invariant when the open-loop system is time-invariant,and drives the feasible trajectories of the system to the origin exponentially. Furthermore, the proposed FAS approach is also extended to the sub-normal system case and the time-delay system case.

关键词： nonholonomic systems feedback stabilization exponential convergence sub-fully actuated systems time-delay systems

exponentially Convergent Multiscale Finite Element Method

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Communications on Applied Mathematics and Computation 2024年第2期6卷 862-878页

作者： Yifan Chen Thomas Y.Hou Yixuan Wang Applied and Computational Mathematics CaltechPasadena 91106USA

We provide a concise review of the exponentially convergent multiscale finite element method(ExpMsFEM)for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave *** ExpMsFEM is built on the non-overlapped domain decomposition in the classical MsFEM while enriching the approximation space systematically to achieve a nearly exponential convergence rate regarding the number of basis *** most generalizations of the MsFEM in the literature,the ExpMsFEM does not rely on any partition of unity *** general,it is necessary to use function representations dependent on the right-hand side to break the algebraic Kolmogorov n-width barrier to achieve exponential ***,there are online and offline parts in the function representation provided by the *** online part depends on the right-hand side locally and can be computed in parallel *** offline part contains basis functions that are used in the Galerkin method to assemble the stiffness matrix;they are all independent of the right-hand side,so the stiffness matrix can be used repeatedly in multi-query scenarios.

关键词： Multiscale method exponential convergence Helmholtz's equation Domain decomposition Nonlinear model reduction

exponential STABILITY OF A MULTI-PARTICLE SYSTEM WITH LOCAL INTERACTION AND DISTRIBUTED DELAY

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Acta Mathematica Scientia 2022年第5期42卷 2165-2187页

作者：刘易成 College of Liberal Arts and Sciences National University of Defense TechnologyChangsha 410073China

For a collective system,the connectedness of the adjacency matrix plays a key role in making the system achieve its emergent feature,such as flocking or *** this paper,we study a nonsymmetric multi-particle system with a constant and local cut-off weight.A distributed communication delay is also introduced into both the velocity adjoint term and the cut-off *** a new observation,we show that the desired multi-particle system undergoes both flocking and clustering behaviors when the eigenvalue 1 of the adjacency matrix is *** this case,the adjacency matrix may lose the *** particular,the number of clusters is discussed by using subspace *** terms of results,for both the non-critical and general neighbourhood situations,some criteria of flocking and clustering emergence with an exponential convergent rate are established by the standard matrix analysis for when the delay is *** a distributed delay is involved,the corresponding criteria are also found,and these small time lags do not change the emergent properties qualitatively,but alter the final value in a nonlinear ***,some previous works[14]are extended.

关键词： semi-simple eigenvalue flocking emergence clustering emergence distributed delay exponential convergence

A Robust Hybrid Spectral Method for Nonlocal Problems with Weakly Singular Kernels

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Numerical Mathematics(Theory,Methods and Applications) 2022年第4期15卷 1041-1062页

作者： Chao Zhang Guoqing Yao Sheng Chen School of Mathematics and Statistics Jiangsu Normal UniversityXuzhou 221116China School of Science University of Shanghai for Science and TechnologyShanghai 200093China Research Center for Mathemaics Beijing Normal UniversityZhuhai 519087China

In this paper,we propose a hybrid spectral method for a type of nonlocal problems,nonlinear Volterra integral equations(VIEs)of the second *** main idea is to use the shifted generalized Log orthogonal functions(GLOFs)as the basis for the first interval and employ the classical shifted Legendre polynomials for other *** method is robust for VIEs with weakly singular kernel due to the GLOFs can efficiently approximate one-point singular functions as well as smooth *** well-posedness and the related error estimates will be *** numerical experiments will verify the theoretical results and show the high-efficiency of the new hybrid spectral method.

关键词： Nonlocal problem Volterra integral spectral element method log orthogonal function Legendre polynomial weak singularity exponential convergence