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Higher-order properties and extensions for indirect MRAC and APPC of linear systems

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Science china(Information Sciences) 2024年第4期67卷 218-238页

作者： Yanjun zhang Zhipeng zhang Jian SUN Lei WANG Kangkang zhang National Key Lab of Autonomous Intelligent Unmanned Systems Beijing Institute of Technology Beijing Institute of Technology Chongqing Innovation Center College of Control Science and Engineering Zhejiang University department of Electrical and Electronic Engineering Imperial College London KIOS Research and Innovation Center of Excellence University of Cyprus

Recently, a reference derived some new higher-order output tracking properties for direct model reference adaptive control(MRAC) of linear time-invariant(LTI) systems: limt→∞ e~((i))(t) = 0, i = 1,..., n~*-1, where n~* and e~((i))(t) denote the relative degree of the system and the i-th derivative of the output tracking error, respectively. However, a naturally arising question involves whether indirect adaptive control(including indirect MRAC and indirect adaptive pole placement control) of LTI systems still has higher-order tracking properties. Such properties have not been reported in the literature. Therefore, this paper provides an affirmative answer to this question. Such higher-order tracking properties are new discoveries since they hold without any additional design conditions and, in particular, without the persistent excitation condition. Given the higher-order properties, a new adaptive control system is developed with stronger tracking features.(1) It can track a reference signal with any order derivatives being unknown.(2. It has higher-order exponential or practical output tracking properties.(3) Finally, it is different from the usual MRAC system, whose reference signal’s derivatives up to the n~* order are assumed to be known. Finally, two simulation examples are provided to verify the theoretical results obtained in this paper.

关键词： higher-order tracking indirect adaptive control model reference adaptive control adaptive pole placement control

On the Limit Cycles of Quadratic Differential Systems

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Acta Mathematica Sinica,English Series 2002年第4期18卷 803-816页

作者： Xiang zhang department of {2., Shanghai Jiaotong University, Shanghai 2.0030, P. R. china department of mathematics Shanghai Jiaotong University Shanghai 200030 P. R. China

In this paper we give the necessary and sufficient conditions for all finite critical points of quadratic differential systems to be weak foci, and solve an open problem proposed by Yanqian Ye.

关键词： Quadratic differential system Limit cycle Ergodicity.

FUZZY PRETOPOLOGICALSPACES, AN EXTENSIONALTOPOLOGICAL EXTENSION OF FTS

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Chinese Annals of mathematics,Series B 1999年第3期20卷 309-316页

作者： zhang DEXUE(department of {2., Sichuan University, Chengdu 610064, china.)(Project supported by the National Natural Science Foundation of china.) Sichuan Univ Dept Math Chengdu 610064 Peoples R China

The category of fuzzy pretopological spaces is introduced, and it is proved that this category is a well-fibred extensional topological construct, and it is a finally dense extension of the category of fuzzy topological spaces. Moreover this category contains both the category of pretopological spaces and the category of probabilistic neighbourhood spaces as simultaneously bireflective and bicoreflective full subcategories.

关键词： Fuzzy topological spaces Fuzzy pretopological spaces Extensional topological category

Tests for nonparametric parts on partially linear single index models

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Science china mathematics 2007年第3期50卷 439-449页

作者： Ri-quan zhang department of Statistics, East{2. Normal University, Shanghai 2.0062.{2. department of mathematics, Shanxi Datong University, Datong 037009,{2. department of Statistics East China Normal University Shanghai 200062China

Tests for nonparametric parts on partially linear single index models are considered in this paper. Based on the estimates obtained by the local linear method, the generalized likelihood ratio tests for the models are established. Under the null hypotheses the normalized tests follow asymptotically the χ2.distribution with the scale constants and the degrees of freedom being independent of the nuisance parameters, which is called the Wilks phenomenon. A simulated example is used to evaluate the performances of the testing procedures empirically.

关键词： local linear method partially linear single index models generalized likelihood ratio test Wilks phenomenon χ 2.distribution 62.10 62.2.

Pseudo almost periodic solutions to parabolic boundary value inverse problems

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Science china mathematics 2008年第7期51卷 1203-1214页

作者： zhang ChuanYi & YANG FengLin department of {2.,Harbin Institute of Technology,Harbin 150001,china 1. department of mathematics Harbin Institute of Technology Harbin 150001 China

We first define the pseudo almost periodic functions in a more general *** we show the existence,uniqueness and stability of pseudo almost periodic solutions of parabolic inverse problems for a type of boundary value ... 详细信息

关键词： pseudo almost periodic function inverse problem parabolic equation boundary value problem

SOME BOUNDARY INCREASING PROPERTIES OF HARMONIC FUNCTIONS IN LIPSCHITZ DOMAIN

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Chinese Annals of mathematics,Series B 1996年第2期17卷 159-166页

作者： zhang YIPING department of {2., Wuhan University, Wuhan 430072. china.Project supported by the National Natural Science Foundation of china. WUHAN UNIV DEPT MATH WUHAN 430072 PEOPLES R CHINA

The object of this paper is to study the non-tangential increasing properties of positiveharmonic function u in Lipschitz domain by means of Martin representation theory. A necessaryand sufficient condition of the control of growth of u near any fixed boundary point is obtained.It is shown that the non-tangential increasing degree of u near a boundary point is exactlythe local degree of its representation measure with respect to the harmonic measure. Someexamples are given.

关键词： Martin representation Harmonic function Harmonic measure

TWO-WEIGHT NORM INEQUALITY FOR IMAGINARY POWERS OF A LAPLACE OPERATOR

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Journal of Systems Science & Complexity 2006年第3期19卷 403-408页

作者： Jianlin zhang department of {2. and Physics,Zhongyuan Institute of Technology,Zhengzhou 450007,china department of {2.,Beijing Institute of Technology,Beijing 100081,china. department of mathematics and Physics Zhongyuan Institute of Technology Zhengzhou 450007 China

We study two-weight norm inequality for imaginary powers of a Laplace operator in R^n, n ≥ 1, especially from weighted Lebesgue space Lv^p（R^n） to weighted Lebesgue space Lμ^p（R^n）, where 1 〈 p 〈 ∞. We prove that the two-weighted norm inequality holds whenever for some t 〉 1, （μ^t, v^t） ∈ Ap, or if （μ, v） ∈Ap, where μ and v^-1/（p-1） satisfy the growth condition and reverse doubling property.

关键词： Ap condition Laplace operator weighted norm inequality.

Equivalent construction of the infinitesimal time translation operator in algebraic dynamics algorithm for partial differential evolution equation

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Science china(Physics,Mechanics & Astronomy) 2010年第8期53卷 1475-1480页

作者： LIU ChengShi department of mathematics, Northeast Petroleum University, Daqing 163318,{2. 1. department of mathematics Northeast Petroleum University Daqing 163318 China

We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.

关键词： algebraic dynamics infinitesimal time translation operator partial differential evolution equation

The Coupled-mode Theory of Grating-assisted Parallel Optical Fiber Cores

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Chinese Journal of Lasers 2002年第1期11卷 52-57页

作者： ZHU Songlin zhang Xianmin CHEN Kangsheng (department of Information & Electronic Engineering, Zhejiang University,{2., china) department of Information & Electronic Engineering Zhejiaiig University Hangzhou 310027

A new coupled-mode formulation is developed for grating-assisted parallel optical fiber cores. The theory is derived from the scalar wave equation by perturbation method. The diffraction caused by grating and coupler in the grating region are both considered. Based on the theory, various experimental phenomena in grating-assisted parallel optical fiber cores can be simulated accurately.

关键词： fiber grating coupled-mode directional coupler