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Distributed optimal consensus of multiple double integrators under bounded velocity and acceleration
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作者 Zhirong QIU Lihua XIE Yiguang HONG 《控制理论与技术:英文版》 EI CSCD 2019年第1期85-98,共14页
This paper studies a distributed optimal consensus problem for multiple double integrators under bounded velocity and acceleration. Assigned with an in dividual and private convex cost which is dependent on the positi... This paper studies a distributed optimal consensus problem for multiple double integrators under bounded velocity and acceleration. Assigned with an in dividual and private convex cost which is dependent on the position, each age nt n eeds to achieve consensus at the optimum of the aggregate cost under bounded velocity and acceleration. Based on relative positions and velocities to neighbor agents, we design a distributed control law by including the integration feedback of position and velocity errors. By employing quadratic Lyapunov functions, we solve the optimal consensus problem of double-integrators when the fixed topology is strongly connected and weight-balanced. Furthermore, if an initial estimate of the optimum can be known, then control gains can be properly selected to achieve an exponentially fast convergence under bounded velocity and acceleration. The result still holds when the relative velocity is not available, and we also discuss an extension for heterogeneous Euler-Lagrange systems by in verse dynamics control. A nu meric example is provided to illustrate the result. 展开更多
关键词 DISTRIBUTED optimization DOUBLE INTEGRATORS BOUNDED VELOCITY BOUNDED input
微分方程解次数的界 预览
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作者 李爱平 《宁夏师范学院学报》 2019年第1期12-17,共6页
针对微分方程解次数界的求解问题,提出了一种用于计算二维非退化多项式微分方程代数解的算法.算法首先基于Moulin Ollagnier证明,将指数写成具有非负整数系统的奇异叶面特征比的线性组合,获得度数为1和2的丢番图方程组,从而确定多项式1... 针对微分方程解次数界的求解问题,提出了一种用于计算二维非退化多项式微分方程代数解的算法.算法首先基于Moulin Ollagnier证明,将指数写成具有非负整数系统的奇异叶面特征比的线性组合,获得度数为1和2的丢番图方程组,从而确定多项式1形式的界.然后对算法基于的定理进行证明,最后利用实例进行验证,说明所提算法的有效性和可行性. 展开更多
关键词 微分方程 次数 有界
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LOW MACH NUMBER LIMIT OF A COMPRESSIBLE NON-ISOTHERMAL NEMATIC LIQUID CRYSTALS MODEL 预览
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作者 樊继山 栗付才 《数学物理学报:B辑英文版》 SCIE CSCD 2019年第2期449-460,共12页
In this paper, we study the low Mach number limit of a compressible nonisothermal model for nematic liquid crystals in a bounded domain. We establish the uniform estimates with respect to the Mach number, and thus pro... In this paper, we study the low Mach number limit of a compressible nonisothermal model for nematic liquid crystals in a bounded domain. We establish the uniform estimates with respect to the Mach number, and thus prove the convergence to the solution of the incompressible model for nematic liquid crystals. 展开更多
关键词 COMPRESSIBLE NON-ISOTHERMAL liquid CRYSTALS BOUNDED domain low MACH number LIMIT
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Thirty years of turbulence study in China 预览
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作者 Bohua SUN 《应用数学和力学:英文版》 SCIE EI CSCD 2019年第2期193-214,共22页
This paper provides a comprehensive introduction to the major progress in transition and turbulence studies in China over the past thirty years.Despite the author’s best efforts,there are some unavoidable omissions.W... This paper provides a comprehensive introduction to the major progress in transition and turbulence studies in China over the past thirty years.Despite the author’s best efforts,there are some unavoidable omissions.We expect that with the continued deepening of turbulence research,Chinese scholars will make increasing contributions in this field,which will certainly have strong influence on the establishment of a China School of Turbulence. 展开更多
关键词 TURBULENCE TRANSITION WALL BOUNDED FLOW
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Wave packet solutions in a bounded equatorial ocean and its interannual and decadal variabilities 预览
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作者 Dongling Zhang Juan Zhu +1 位作者 Xu Lu Ming Zhang 《海洋学报:英文版》 SCIE CAS CSCD 2019年第3期45-59,共15页
Linearized shallow water perturbation equations with approximation in an equatorial β plane are used to obtain the analytical solution of wave packet anomalies in the upper bounded equatorial ocean. The main results ... Linearized shallow water perturbation equations with approximation in an equatorial β plane are used to obtain the analytical solution of wave packet anomalies in the upper bounded equatorial ocean. The main results are as follows. The wave packet is a superposition of eastward travelling Kelvin waves and westward travelling Rossby waves with the slowest speed, and satisfies the boundary conditions of eastern and western coasts, respectively.The decay coefficient of this solution to the north and south sides of the equator is inversely proportional only to the phase velocity of Kelvin waves in the upper water. The oscillation frequency of the wave packet, which is also the natural frequency of the ocean, is proportional to its mode number and the phase velocity of Kelvin waves and is inversely proportional to the length of the equatorial ocean in the east-west direction. The flow anomalies of the wave packet of Mode 1 most of the time appear as zonal flows with the same direction. They reach the maximum at the center of the equatorial ocean and decay rapidly away from the equator, manifested as equatorially trapped waves. The flow anomalies of the wave packet of Mode 2 appear as the zonal flows with the same direction most of the time in half of the ocean, and are always 0 at the center of the entire ocean which indicates stagnation, while decaying away from the equator with the same speed as that of Mode 1. The spatial structure and oscillation period of the wave packet solution of Mode 1 and Mode 2 are consistent with the changing periods of the surface spatial field and time coefficient of the first and second modes of complex empirical orthogonal function(EOF)analysis of flow anomalies in the actual equatorial ocean. This indicates that the solution does exist in the real ocean, and that El Ni?o-Southern Oscillation(ENSO) and Indian Ocean dipole(IOD) are both related to Mode 2.After considering the Indonesian throughflow, we can obtain the length of bounded equatorial ocean by taking the sum of that of the t 展开更多
关键词 BOUNDED EQUATORIAL OCEAN WAVE packet SOLUTIONS DECADAL variability Kelvin WAVE Rossby WAVE
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Quadratic Stabilization of Switched Uncertain Linear Systems:A Convex Combination Approach 预览
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作者 Yufang Chang Guisheng Zhai +1 位作者 Bo Fu Lianglin Xiong 《自动化学报:英文版》 CSCD 2019年第5期1116-1126,共11页
We consider quadratic stabilization for a class of switched systems which are composed of a finite set of continuoustime linear subsystems with norm bounded uncertainties. Under the assumption that there is no single ... We consider quadratic stabilization for a class of switched systems which are composed of a finite set of continuoustime linear subsystems with norm bounded uncertainties. Under the assumption that there is no single quadratically stable subsystem, if a convex combination of subsystems is quadratically stable, then we propose a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched linear system is quadratically stable. When the state information is not available, we extend the discussion to designing an outputdependent switching law by constructing a robust Luenberger observer for each subsystem. 展开更多
关键词 CONVEX combination limear matrix INEQUALITIES (LMIs) norm BOUNDED uncertainties output-dependent switching quadratic stabilization state-dependent SWITCHING SWITCHED uncertain linear systems(SULS)
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三阶非线性模糊差分方程动力学行为分析 预览
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作者 张千宏 王贵英 《西南师范大学学报:自然科学版》 CAS 北大核心 2019年第7期1-7,共7页
研究一类三阶非线性模糊差分方程正解的存在性及渐近行为xn+1=xn-2/A+xn-2xn-1xn,n=0,1,…其中(xn)是正模糊数数列,A及初始值x-2,x-1,x0是正模糊数.最后给出数值例子以验证理论结论的正确性.
关键词 模糊差分方程 平衡点 有解性 持久性 渐近稳定
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Dynamical behaviors of the generalized hematopoiesis model with discontinuous harvesting terms
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作者 Fanchao Kong 《生物数学学报:英文版》 2019年第1期195-231,共37页
This paper is concerned with the generalized hematopoiesis model with discontinuous harvesting terms.Under the framework of Filippov solution,by means of the differential inclusions and the topological degree theory i... This paper is concerned with the generalized hematopoiesis model with discontinuous harvesting terms.Under the framework of Filippov solution,by means of the differential inclusions and the topological degree theory in set-valued analysis,we have established the existence of the bounded positive periodic solutions for the addressed models.After that,based on the nonsmooth analysis theory w让 h Lyapunov-like approach,we employ a novel argument and derive some new criteria on the uniqueness,global exponential stability of the addressed models and convergence of the corresponding autonomous case of the addressed models.Our results extend previous works on hematopoiesis model to the discontinuous harvesting terms and some corresponding results in the literature can be enriched and extended.In addition,typical examples with numerical simulations are given to illustrate the feasibility and validity of obtained results. 展开更多
关键词 Positive periodic solution BOUNDED DISCONTINUOUS HARVESTING TERMS topological degree theory Lyapunov-like approach global EXPONENTIAL stability convergence
Uncertain Opinion Evolution with Bounded Confidence Effects in Social Networks
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作者 Min Zhan Haiming Liang +1 位作者 Zhaogang Ding Yucheng Dong 《系统科学与系统工程学报:英文版》 SCIE EI CSCD 2019年第4期494-509,共16页
When people express their opinions for an issue, they can express both exact opinions and uncertain opinions, such as numerical interval opinions. Moreover, social network is a crucial medium of opinion interaction an... When people express their opinions for an issue, they can express both exact opinions and uncertain opinions, such as numerical interval opinions. Moreover, social network is a crucial medium of opinion interaction and evolution. In this paper, uncertain opinion evolution with bounded confidence effects in social networks is investigated by theoretical demonstration and numerical examples analyses, and experiments simulations analyses. Theoretical results show when all the agents are with uncertainty tolerances, then the ratios of agents expressing uncertain opinions are impossible to decrease, even increase, as time increases;while when all the agents are without uncertainty tolerances, then the ratios of agents expressing uncertain opinions are impossible to increase, even decrease, as time increases. Moreover, the average widths of uncertain opinions are always smaller than the maximum opinion width of all the initial opinions among agents. Experiments simulations results show different ratios of agents with uncertainty tolerances and different ratios of agents expressing uncertain opinions have strong impact on the ratios of the agents expressing the uncertain opinions in the stable state, and the average widths of uncertain opinions in the stable state. 展开更多
关键词 OPINION evolution uncertainty BOUNDED CONFIDENCE SOCIAL network
Robust topology optimization of hinge-free compliant mechanisms with material uncertainties based on a non-probabilistic field model
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作者 Junjie ZHAN Yangjun LUO 《机械工程前沿:英文版》 CSCD 2019年第2期201-212,共12页
This paper presents a new robust topology optimization framework for hinge-free compliant mechanisms with spatially varying material uncertainties,which are described using a non-probabilistic bounded field model.Boun... This paper presents a new robust topology optimization framework for hinge-free compliant mechanisms with spatially varying material uncertainties,which are described using a non-probabilistic bounded field model.Bounded field uncertainties are efficiently represented by a reduced set of uncertain-but-bouncled coeflficients on the basis of the series expansion method.Robust topology optimization of compliant mechanisms is then defined to minimize the variation in output displacement under constraints of the mean displacement and predefined material volume.The nest optimization problem is solved using a gradient-based optimization algorithm.Numerical examples are presented to illustrate the effectiveness of the proposed method for circumventing hinges in topology optimization of compliant mechanisms. 展开更多
关键词 compliant mechanisms ROBUST topology optimization HINGES uncertainty BOUNDED field
Standing Waves for Discrete Nonlinear Schrodinger Equations with Nonperiodic Bounded Potentials
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作者 Tie-shan HE Meng ZHANG +1 位作者 Kai-hao LIANG Peng-fei GUO 《应用数学学报:英文版》 SCIE CSCD 2019年第2期374-385,共12页
In this paper, we investigate standing waves in discrete nonlinear Schrodinger equations with nonperiodic bounded potentials. By using the critical point theory and the spectral theory of self-adjoint operators, we pr... In this paper, we investigate standing waves in discrete nonlinear Schrodinger equations with nonperiodic bounded potentials. By using the critical point theory and the spectral theory of self-adjoint operators, we prove the existence and infinitely many sign-changing solutions of the equation. The results on the exponential decay of standing waves are also provided. 展开更多
关键词 DISCRETE nonlinear SCHRODINGER equation STANDING wave Nonperiodic BOUNDED potential: Signchanging solution CRITICAL point theory
Infimum of the Spectrum of Laplace-Beltrami Operator on Classical Bounded Symmetric Domains with Bergman Metric
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作者 Sujuan LONG Kezan LI 《数学研究及应用:英文版》 CSCD 2019年第1期43-50,共8页
In this paper,we estimate the infimum of the spectrum of the Laplace-Beltrami operator with Kahler metric on the classical bounded symmetric domains.We will give an explicit range for the infimum of the spectrum of th... In this paper,we estimate the infimum of the spectrum of the Laplace-Beltrami operator with Kahler metric on the classical bounded symmetric domains.We will give an explicit range for the infimum of the spectrum of the Laplace-Beltrami operator on the second type classical bounded symmetric domains.In particular,for those domains with rank 1,we obtain an explicit formula,which agrees with a previously known result. 展开更多
关键词 Laplace-Beltrami operator CLASSICAL BOUNDED SYMMETRIC DOMAINS KAHLER metric
关于幂级数收敛半径求法的注记 预览
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作者 彭娟 范周田 杨蓉 《大学数学》 2019年第2期106-109,共4页
幂级数是微积分应用的重要理论基础,其中收敛半径的求法是学习相关内容的重点和难点.面向工科的高等数学教学中,通常限于介绍求比较简单的幂级数的收敛半径的方法,对于一般的幂级数,由于涉及上极限的理论,高等数学中不做讨论.本文从有... 幂级数是微积分应用的重要理论基础,其中收敛半径的求法是学习相关内容的重点和难点.面向工科的高等数学教学中,通常限于介绍求比较简单的幂级数的收敛半径的方法,对于一般的幂级数,由于涉及上极限的理论,高等数学中不做讨论.本文从有界的角度讨论幂级数的收敛半径问题,避开了上极限问题的困难,所得结果可用于求任意幂级数的收敛半径. 展开更多
关键词 幂级数 收敛半径 上极限 有界
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On the Origin and Numerical Range of Bounded Operators
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作者 Xiao Hong WU Jun Jie HUANG ALATANCANG 《数学学报:英文版》 SCIE CSCD 2019年第10期1715-1722,共8页
Numerical range has an important applications on spectrum distribution of operators. In this paper, we devoted to characterizing operators whose numerical range contains the origin. Some necessary and sufficient condi... Numerical range has an important applications on spectrum distribution of operators. In this paper, we devoted to characterizing operators whose numerical range contains the origin. Some necessary and sufficient conditions are given by operator decomposition technique and constructive methods. Furthermore, the closeness of the numerical range of a given operator is also investigated. 展开更多
关键词 BOUNDED LINEAR OPERATOR NUMERICAL RANGE ORIGIN
“有界/无界”理论研究述评 预览
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作者 杜广慧 《唐山师范学院学报》 2019年第5期18-22,共5页
“有界/无界”理论源于西方的认知语言学,沈家煊先生较早将其引入汉语学界,并对其作了较为充分的说明。目前,汉语学界关于“有界/无界”理论的探讨主要集中在有界性成分与无界性成分、词类界性上,研究还不够充分,也不够系统。存在的问... “有界/无界”理论源于西方的认知语言学,沈家煊先生较早将其引入汉语学界,并对其作了较为充分的说明。目前,汉语学界关于“有界/无界”理论的探讨主要集中在有界性成分与无界性成分、词类界性上,研究还不够充分,也不够系统。存在的问题主要是“有界/无界”的标准问题、句法问题还是词法问题、解释力问题、有界化手段问题等。 展开更多
关键词 有界 无界 有界化
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Existence and Dynamics of Bounded Traveling Wave Solutions to Getmanou Equation
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作者 温振庶 《理论物理通讯:英文版》 SCIE CAS CSCD 2018年第12期672-676,共5页
In this paper,we study the existence and dynamics of bounded traveling wave solutions to Getmanou equations by using the qualitative theory of differential equations and the bifurcation method of dynamical systems.We ... In this paper,we study the existence and dynamics of bounded traveling wave solutions to Getmanou equations by using the qualitative theory of differential equations and the bifurcation method of dynamical systems.We show that the corresponding traveling wave system is a singular planar dynamical system with two singular straight lines,and obtain the bifurcations of phase portraits of the system under different parameters conditions.Through phase portraits,we show the existence and dynamics of several types of bounded traveling wave solutions including solitary wave solutions,periodic wave solutions,compactons,kink-like and antikink-like wave solutions.Moreover,the expressions of solitary wave solutions are given.Additionally,we confirm abundant dynamical behaviors of the traveling wave s olutions to the equation,which are summarized as follows:i) We confirm that two types of orbits give rise to solitary wave solutions,that is,the homoclinic orbit passing the singular point,and the composed homoclinic orbit which is comprised of two heteroclinic orbits and tangent to the singular line at the singular point of associated system.ii) We confirm that two types of orbits correspond to periodic wave solutions,that is,the periodic orbit surrounding a center,and the homoclinic orbit of associated system,which is tangent to the singular line at the singular point of associated system. 展开更多
关键词 getmanou EQUATION BOUNDED TRAVELING wave solutions EXISTENCE BIFURCATIONS DYNAMICS
An Exploration of the Mechanism of Educational Scientific Decision-making in View of Bounded Rationality 预览
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作者 ZHU Mei-xia 《文学与艺术研究:英文版》 2018年第7期1103-1108,共6页
The scientific decision-making of education policies is not absolutely a complete rational process.The bounded rationality which takes rationality as the judgement standard is the essential connotation of the scientif... The scientific decision-making of education policies is not absolutely a complete rational process.The bounded rationality which takes rationality as the judgement standard is the essential connotation of the scientific decision-making of education policies.Therefore,based on this view and through shaping reasonable education policy values,this research gives full play to the driving force of educational scientific research on education policies and designs effective education decision-making information content and running agenda,thus optimizing the weigh principle of education policy proposals,advocating risk assessment and practice of education decisions,constructing institutional rationality of educational scientific decision-making,and finally realizing the rationality and scientificity of education policy decision-making. 展开更多
关键词 BOUNDED RATIONALITY EDUCATION activity EDUCATION DECISION-MAKING EXPLORATION
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Robust controller design for compound control missile with fixed bounded convergence time 预览
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作者 YUN Yuhang TANG Shengjing +1 位作者 GUO Jie SHANG Wei 《系统工程与电子技术:英文版》 SCIE EI CSCD 2018年第1期116-133,共18页
A robust controller for bank to turn (BTT) missiles with aerodynamic fins and reaction jet control system (RCS) is developed based on nonlinear control dynamic models comprising couplings and aerodynamic uncertainties... A robust controller for bank to turn (BTT) missiles with aerodynamic fins and reaction jet control system (RCS) is developed based on nonlinear control dynamic models comprising couplings and aerodynamic uncertainties. The fixed time convergence theory is incorporated with the sliding mode control technique to ensure that the system tracks the desired command within uniform bounded time under different initial conditions. Unlike previous terminal sliding mode approaches, the bound of settling time is independent of the initial state, which means performance metrics like convergence rate can be predicted beforehand. To reduce the burden of control design in terms of robustness, extended state observer (ESO) is introduced for uncertainty estimation with the output substituted into the controller as feedforward compensation. Cascade control structure is employed with the proposed control law and therein the compound control signal is obtained.Afterwards, control inputs for two kinds of actuators are allocated on the basis of their inherent characteristics. Finally, a number of simulations are carried out and demonstrate the effectiveness of the designed controller. 展开更多
关键词 reaction jet CONTROL compound CONTROL fixed BOUNDED convergence time SLIDING mode CONTROL extended state OBSERVER (ESO)
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单位球上Dirichlet型空间到Zμ型空间的积分型算子 预览 被引量:2
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作者 赵艳辉 张学军 《数学物理学报:A辑》 CSCD 北大核心 2017年第2期217-227,共11页
该文利用泛函分析以及多复变的方法,研究了单位球B上Dirichlet型空间Dp到Zygmund型空间乙的积分型算子的有界性和紧性问题.获得了单位球上Dirichlet型空间到Zygmund型空间的积分型算子为有界算子和紧算子的充要条件.
关键词 DIRICHLET型空间 ZYGMUND型空间 积分型算子 有界性 紧性
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关于带有“!”号数列极限的求法 预览 被引量:1
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作者 张海涛 陈慧琴 《高等数学研究》 2017年第6期24-25,41共3页
本文主要介绍了带有“!”号数列极限的证明和计算方法,如“£一N”定义法、平均收敛公式法、迫敛定理法和利用沃利斯(Wallis)公式法,这对掌握数列极限的学习提供一个参考.
关键词 数列 单调 有界 级数
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