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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

Distributed accelerated optimization algorithms:Insights from an ODE

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Science China(Technological Sciences) 2020年第9期63卷 1647-1655页

作者： CHEN RuiJuan YANG Tao CHAI Tian You School of Artificial Intelligence and Automation Hluazhong University of Science and TechnologyWuhan 430074China State Key Laboratory of Synthetical Automation for Process Industries Northeastern UniversityShenyang 110819China

In this paper, we consider the distributed optimization problem, where the goal is to minimize the global objective function formed by a sum of agents' local smooth and strongly convex objective functions, over undirected connected graphs. Several distributed accelerated algorithms have been proposed for solving such a problem in the existing literature. In this paper, we provide insights for understanding these existing distributed algorithms from an ordinary differential equation(ODE) point of view. More specifically, we first derive an equivalent second-order ODE, which is the exact limit of these existing algorithms by taking the small step-size. Moreover, focusing on the quadratic objective functions, we show that the solution of the resulting ODE exponentially converges to the unique global optimal solution. The theoretical results are validated and illustrated by numerical simulations.

关键词： distributed accelerated optimization algorithms exponential convergence ordinary differential equation

A SPECTRAL METHOD FOR PANTOGRAPH-TYPE DELAY DIFFERENTIAL EQUATIONS AND ITS convergence ANALYSIS

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Journal of Computational Mathematics 2009年第2期27卷 254-265页

作者： Ishtiaq Ali Hermann Brunner Institute of Computational Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Mathematics COMSA TS Institute of Information Technology IslamabadPakistan Hermann Brunner Department of Mathematics and Statistics Memorial University of NewfoundlandSt.John’sCanada Department of Mathematics Hong Kong Baptist UniversityHong KongChina

We propose a novel numerical approach for delay differential equations with vanishing proportional delays based on spectral methods. A Legendre-collocation method is employed to obtain highly accurate numerical approximations to the exact solution. It is proved theoretically and demonstrated numerically that the proposed method converges exponentially provided that the data in the are smooth. given pantograph delay differential equation

关键词： Spectral methods Legendre quadrature formula Pantograph-type delay differential equations Error analysis exponential convergence