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Wuhan University Journal of Natural Sciences 2000年第3期5卷 265-270页

作者： Ying Gu\|liang Department of Mathematics, Xianning Teachers’ College, Xia nning 437005,China Department of Mathematics Xianning Teachers' College Xianning China

We studied the asymptotic behavior of solutions to the initial boundary value problem on the spatial interval [0,1] for a one-dimensional simplified gydrodynamic model for semiconductors wheng(t)→b *, and proved the unique global existence of smooth solutions to the initial boundary problem. We also show that the solutions converge to the corresponding steady-state solutions time-asymptotically by introducing the suitable shift functions.

关键词： semiconductor hydrodynamic model asymptotic convergence

A Modified Integral Global Optimization Method and Its asymptotic convergence

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Acta Mathematicae Applicatae Sinica 2009年第2期25卷 283-290页

作者： Zheng Peng Ya-jun Shen Dong-hua Wu Department of mathematics Nanjing University Nanjing 210093 China Department of mathematics Shanghai University Shanghai 200444 China

In this paper, we propose a new integral global optimization algorithm for finding the solution of continuous minimization problem, and prove the asymptotic convergence of this algorithm. In our modified method we use variable measure integral, importance sampling and main idea of the cross-entropy method to ensure its convergence and efficiency. Numerical results show that the new method is very efficient in some challenging continuous global optimization problems.

关键词： Continuous global optimization modified integral global optimization method asymptotic convergence

Precision motion control for electro-hydraulic axis systems under unknown time-variant parameters and disturbances

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Chinese Journal of Aeronautics 2024年第1期37卷 463-471页

作者： Xiaowei YANG Yaowen GE Wenxiang DENG Jianyong YAO School of Mechanical Engineering Nanjing University of Science and TechnologyNanjing 210094China

This article focuses on asymptotic precision motion control for electro-hydraulic axis systems under unknown time-variant parameters,mismatched and matched *** from the traditional adaptive results that are applied to dispose of unknown constant parameters only,the unique feature is that an adaptive-gain nonlinear term is introduced into the control design to handle unknown time-variant *** both mismatched and matched disturbances existing in electro-hydraulic axis systems can also be addressed in this *** skillful integration of the backstepping technique and the adaptive control,a synthesized controller framework is successfully developed for electro-hydraulic axis systems,in which the coupled interaction between parameter estimation and disturbance estimation is ***,this designed controller has the capacity of low-computation costs and simpler parameter tuning when compared to the other ones that integrate the adaptive control and observer/estimator-based technique to dividually handle parameter uncertainties and ***,a nonlinear filter is designed to eliminate the“explosion of complexity”issue existing in the classical back-stepping *** stability analysis uncovers that all the closed-loop signals are bounded and the asymptotic tracking performance is also ***,contrastive experiment results validate the superiority of the developed method as well.

关键词： Adaptive control asymptotic convergence Electro-hydraulic axis system Precision motion control Unknown time-variant parameters and disturbances

Nonlinear Extrapolation Estimates of π

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 91-108页

作者： Wen-qing Xu Sha-sha Wang Da-chuan Xu Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing100124China Department of Mathematics and Statistics California State UniversityLong BeachCalifornia90840USA Department of Mathematics and Physics Shijiazhuang Tiedao UniversityShijiazhuang050043China

The classical Archimedean approximation of π uses the semiperimeter or area of regular polygons inscribed in or circumscribed about a unit circle in R~2 and it is well-known that by using linear combinations of these basic estimates,modern extrapolation techniques can greatly speed up the approximation ***,when n vertices are randomly selected on the circle,the semiperimeter and area of the corresponding random inscribed and circumscribing polygons are known to converge to π almost surely as n→∞,and by further applying extrapolation processes,faster convergence rates can also be achieved through similar linear combinations of the semiperimeter and area of these random *** this paper,we further develop nonlinear extrapolation methods for approximating π through certain nonlinear functions of the semiperimeter and area of such *** focus on two types of extrapolation estimates of the forms χ_n=S_n~αA_n~β and Y_n(p)=(αS_n~p+βA_n~p)~(1/p) where α+β=1,p≠0,and Sn and An respectively represents the semiperimeter and area of a random n-gon inscribed in the unit circle in R~2,and Xn may be viewed as the limit of Y_n(p) when p→*** deriving probabilistic asymptotic expansions with carefully controlled error estimates for Xn and Y_n(p),we show that the choice α=4/3,β=-1/3 minimizes the approximation error in both cases,and their distributions are also asymptotically normal.

关键词： Archimedean polygons random polygons approximations ofπ extrapolation processes asymptotic convergence

Observer-based motion axis control for hydraulic actuation systems

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中国航空学报:英文版 2023年第9期36卷 408-415页

作者： Xiaowei YANG Yaowen GE Wenxiang DENG Jianyong YAO School of Mechanical Engineering Nanjing University of Science and TechnologyNanjing 210094China

Unknown dynamics including mismatched mechanical dynamics(i.e.,parametric uncertainties,unmodeled friction and external disturbances)and matched actuator dynamics(i.e.,pressure and flow characteristic uncertainties)broadly exist in hydraulic actuation systems(HASs),which can hinder the achievement of high-precision motion axis *** surmount the practical issue,an observer-based control framework with a simple structure and low computation is developed for ***,a simple observer is utilized to estimate mismatched and matched unknown dynamics for feedforward *** combining the backstepping design and adaptive control,an appropriate observer-based composite controller is provided,in which nonlinear feedback terms with updated gains are adopted to further improve the tracking ***,a smooth nonlinear filter is introduced to shun the“explosion of complexity”and attenuate the impact of sensor noise on control *** a result,this synthesized controller is more suitable for practical *** analysis uncovers that the developed controller assures the asymptotic convergence of the tracking *** merits of the proposed approach are validated via comparative experiment results applied in an HAS with an inertial load as well.

关键词： Adaptive control asymptotic convergence Hydraulic actuation system Sensor noise Unknown dynamics compensation

Enhancing Iterative Learning Control With Fractional Power Update Law

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IEEE/CAA Journal of Automatica Sinica 2023年第5期10卷 1137-1149页

作者： Zihan Li Dong Shen Xinghuo Yu the School of Mathematics Renmin University of ChinaBeijing 100872China the School of Engineering RMIT UniversityMelbourne VIC 3001Australia

The P-type update law has been the mainstream technique used in iterative learning control(ILC)systems,which resembles linear feedback control with asymptotical *** recent years,finite-time control strategies such as terminal sliding mode control have been shown to be effective in ramping up convergence speed by introducing fractional power with *** this paper,we show that such mechanism can equally ramp up the learning speed in ILC *** first propose a fractional power update rule for ILC of single-input-single-output linear systems.A nonlinear error dynamics is constructed along the iteration axis to illustrate the evolutionary converging *** the nonlinear mapping approach,fast convergence towards the limit cycles of tracking errors inherently existing in ILC systems is *** limit cycles are shown to be tunable to determine the steady *** simulations are provided to verify the theoretical results.

关键词： asymptotic convergence convergence rate finiteiteration tracking fractional power learning rule limit cycles

Finite-time formation control for first-order multi-agent systems with region constraints

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Frontiers of Information Technology & Electronic Engineering 2021年第1期22卷 134-140页

作者： Zhengquan YANG Xiaofang PAN Qing ZHANG Zengqiang CHEN College of Science Civil Aviation University of ChinaTianjin 300300China College of Artificial Intelligence Nankai UniversityTianjin 300350China

In this study,the finite-time formation control of multi-agent systems with region constraints is *** agents have first-order dynamics and a common target area.A novel control algorithm is proposed using local information and *** the communication graph is undirected and connected and the desired framework is rigid,it is proved that the controller can be used to solve the formation problem with a target *** is,all agents can enter the desired region in finite time while reaching and maintaining the desired formation ***,a numerical example is given to illustrate the results.

关键词： Finite-time formation Multi-agent system asymptotic convergence Set constraint Lyapunov theorem

Stochastic level-value approximation for quadratic integer convex programming

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Applied Mathematics and Mechanics(English Edition) 2008年第6期29卷 801-809页

作者：彭拯邬冬华 Department of Mathematics Shanghai UniversityShanghai 200444P.R.China

We propose a stochastic level value approximation method for a quadratic integer convex minimizing problem in this paper. This method applies an importance sampling technique, and make use of the cross-entropy method to update the sample density functions. We also prove the asymptotic convergence of this algorithm, and report some numerical results to illuminate its effectiveness.

关键词： quadratic integer convex programming stochastic level value approximation cross-entropy method asymptotic convergence

Inertial projection algorithms for convex feasibility problem

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Journal of Systems Engineering and Electronics 2012年第5期23卷 734-740页

作者： Yazheng Dang Yan Gao Lihua Li School of Management University of Shanghai for Science and Technology Shanghai 200093 P. R. China School of Computer Science and Technology Henan Polytechnic University Henan 454001 P. R. China

The purpose of this paper is to apply inertial technique to string averaging projection method and block-iterative projection method in order to get two accelerated projection algorithms for solving convex feasibility *** with the existing accelerated methods for solving the problem,the inertial technique employs a parameter sequence and two previous iterations to get the next iteration and hence improves the flexibility of the *** asymptotic convergence results are presented under some suitable *** simulations illustrate that the new methods have better convergence than the general projection *** presented algorithms are inspired by the inertial proximal point algorithm for finding zeros of a maximal monotone operator.

关键词： convex feasibility problem inertial technique string averaging block iteration asymptotic convergence

Periodic Adaptive Identification and Control for a class of Discrete Time-varying Systems

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Periodic Adaptive Identification and Control for a class of ...