检索结果-内蒙古大学图书馆

piecewise linear-approximation FOR HEREDITARY CONTROL-PROBLEMS

SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1990年第1期28卷 70-96页

作者： PROPST, G NASA LANGLEY RES CTRINST COMP APPL SCI & ENGNHAMPTONVA 23665

This paper presents finite-dimensional approximations for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems, when a quadratic cost integral must be minimjzed subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in the case where the cost integral ranges over a finite time interval, as well as in the case where it ranges over an infinite time interval. The arguments in the last case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space $\mathbb{R}^n \times L^2 $ and the favorable eigenvalue behavior of the piecewise linear approximations.

关键词： 34K35 65L60 93C15 hereditary control problem piecewise linear approximation uniform stability

来源：评论

学校读者我要写书评

暂无评论

piecewise linear approximation of smooth compact fibers

引用

JOURNAL OF COMPLEXITY 2002年第2期18卷 547-556页

作者： Allgower, EL Sommese, AJ Colorado State Univ Dept Math Ft Collins CO 80523 USA Univ Notre Dame Dept Math Notre Dame IN 46556 USA

Let H : R-N --> R-m be a twice differentiable map. Let N : = n + m. Assume that the fiber F : = H-1(y(0)) of H over a point y(0) is an element of R-m is a compact n-dimensional differentiable manifold and that partial derivativeH is of maximal rank in a neighborhood of F. Works of Allgower and Gnutzmann, and of Allgower and Schmidt give an algorithm to find a global piecewise linear approximation of F based on a triangulation of R-N. Several authors have given algorithms for obtaining a piecewise linear approximation of F in a way that does not depend on the triangulation in R-N. This effects a reduction of the combinatorial complexity from O(N!) to 0(n!). but the approximations are not global. In this paper, a probability one algorithm is given, which, given H, F, N, m as above, uses homotopy continuation to construct a differentiable map (H) over tilde : R2n-1 --> Rn+1 with a compact differentiable manifold (F) over tilde : = (H) over tilde (-1)(0), which is diffeomorphic to F by an explicit diffeomorphism, and with partial derivative(H) over tilde of maximal rank in a neighborhood of (F) over tilde. This reduces the problem when N > 2n + 1 to the known piecewise linear algorithm in R2n+1 at the simpler expense of carrying out a well-behaved homotopy continuation starting at vertices of the simplices of the triangulation of a neighborhood of pi(F) subset of R2n+1, where pi : R-N --> R2n-1 is a generic linear projection. Consequently, a global algorithm is obtained with a combinatorial complexity of O((2n+1)!). (C) 2002 Elsevier Science (USA).

关键词： piecewise linear approximation homotopy continuation

来源：评论

学校读者我要写书评

暂无评论

piecewise linear approximation of empirical distributions under a Wasserstein distance constraint

引用

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2018年第16期88卷 3193-3216页

作者： Arbenz, Philipp Guevara-Alarcon, William SCOR Switzerland Ltd Zurich Switzerland Swiss Fed Inst Technol Zurich Switzerland Univ Lausanne Extranef Of 105 CH-1015 Lausanne Switzerland

Big data applications and Monte Carlo simulation results can nowadays easily contain data sets in the size of millions of entries. We consider the situation when the information on a large univariate data set or sample needs to be preserved, stored or transferred. We suggest an algorithm to approximate a univariate empirical distribution through a piecewise linear distribution which requires significantly less memory to store. The approximation is chosen in a computationally efficient manner, such that it preserves the mean, and its Wasserstein distance to the empirical distribution is sufficiently small.

关键词： Monte Carlo simulation empirical distribution piecewise linear approximation Wasserstein distance compression

来源：评论

学校读者我要写书评

暂无评论

piecewise linear approximation of Fuzzy Numbers Preserving the Support and Core

Piecewise Linear Approximation of Fuzzy Numbers Preserving t...

引用

15th International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU)

作者： Coroianu, Lucian Gagolewski, Marek Grzegorzewski, Przemyslaw Firozja, M. Adabitabar Houlari, Tahereh Univ Oradea Dept Math & Informat 1 Univ St Oradea 410087 Romania Polish Acad Sci Syst Res Inst Warsaw Poland Warsaw Univ Technol Fac Math & Informat Sci Warsaw Poland Islamic Azad Univ Dept Math Tehran Iran Damghan Univ Sch Math & Comp Sci Damghan Iran

ISBN: (纸本)9783319088556;9783319088549

A reasonable approximation of a fuzzy number should have a simple membership function, be close to the input fuzzy number, and should preserve some of its important characteristics. In this paper we suggest to approximate a fuzzy number by a piecewise linear 1-knot fuzzy number which is the closest one to the input fuzzy number among all piecewise linear 1-knot fuzzy numbers having the same core and the same support as the input. We discuss the existence of the approximation operator, show algorithms ready for the practical use and illustrate the considered concepts by examples. It turns out that such an approximation task may be problematic.

关键词： approximation of fuzzy numbers core fuzzy number piecewise linear approximation support

来源：评论

学校读者我要写书评

暂无评论

piecewise linear approximation Minimum Current Trajectory for Dual Active Full-bridge Bidirectional DC-DC Converter 9

Piecewise Linear Approximation Minimum Current Trajectory fo...

引用

IEEE 9th International Power Electronics and Motion Control Conference (IPEMC-ECCE Asia)

作者： Luo, Ningyu Wen, Huiqing Bu, Qinglei Xian Jiaotong Liverpool Univ Dept Elect & Elect Engn Suzhou 215123 Peoples R China

ISBN: (纸本)9781728153018

This paper will introduce a controller based on the piecewise linear approximation minimum current trajectory(PWL-MCT) for the series resonant dual active-bridge(SR-DAB) dc-dc converters based on the minimum current trajectory(MCT). The linear approximation is based on the minimum current trajectory, thus it can maintain an approximately optimized switching loss at full working range. The power flow through the Dual active-bridge DC-DC converter is controlled by adjusting the duty factor for both primary side and secondary side of the converter and the phase shifting angle between each side s voltage signal simultaneously. While applying the proposed controller, the tank rms current optimizing effect of this converter was proved to perform closely enough to the one applied with original minimum current trajectory controller.

关键词： DAB series resonant tank rms current minimum current trajectory piecewise linear approximation

来源：评论

学校读者我要写书评

暂无评论

piecewise linear approximation by the Method of Worst Segment Division

引用

LOBACHEVSKII JOURNAL OF MATHEMATICS 2021年第12期42卷 2969-2979页

作者： Sukiasyan, H. S. Natl Acad Sci Republ Armenia Inst Math Yerevan 0019 Armenia Natl Polytech Univ Armenia Yerevan Armenia

The finite element method for numerical solving two-dimensional boundary value problem is based on domain triangulation and piecewise linear approximation. The present paper describes how to minimize the number of triangulation vertices without exceeding the given level of the approximation error. The paper proposes a method for constructing piecewise linear approximations for continuous two-dimensional functions by dividing the ''worst'' segment. The possibilities of applying the proposed method in solving boundary value problems are investigated. The main theorem gives a sufficient condition on the minimized functional so that the best mesh would be the Delaunay triangulation. An example of a numerical solution of the Maxwell equation of the electromagnetic field using the method of the worst segment division with Delaunay triangulation is given.

关键词： boundary value problem finite element method piecewise linear approximation Dealaunay triangulation recursive algorithm

来源：评论

学校读者我要写书评

暂无评论

引用

EXPERT SYSTEMS WITH APPLICATIONS 2011年第12期38卷 14732-14743页

作者： Li, Haili Guo, Chonghui Qiu, Wangren Dalian Univ Technol Inst Syst Engn Dalian 116024 Peoples R China Dalian Univ Technol Res Ctr Informat & Control Dalian 116024 Peoples R China

We propose a new method to calculate the similarity of time series based on piecewise linear approximation (PLA) and derivative dynamic time warping (DDTW). The proposed method includes two phases. One is the divisive approach of piecewise linear approximation based on the middle curve of original time series. Apart from the attractive results, it can create line segments to approximate time series faster than conventional linear approximation. Meanwhile, high dimensional space can be reduced into a lower one and the line segments approximating the time series are used to calculate the similarity. In the other phase, we utilize the main idea of DDTW to provide another similarity measure based on the line segments just we got from the first phase. We empirically compare our new approach to other techniques and demonstrate its superiority. Crown Copyright (C) 2011 Published by Elsevier Ltd. All rights reserved.

关键词： Similarity measure Dynamic time warping piecewise linear approximation Time series mining

来源：评论

学校读者我要写书评

暂无评论

AN ADAPTIVE REDUCTION PROCEDURE FOR THE piecewise linear-approximation OF DIGITIZED-CURVES

引用

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 1989年第9期11卷 967-973页

作者： FAHN, CS WANG, JF LEE, JY Dept. of Electr. Eng. Nat. Cheng Kung Univ. Tainan Taiwan

A new algorithm is presented for the piecewise linear approximation of two-dimensional digitized curves against a square grid. The algorithm utilizes an adaptive reduction procedure in two approximation phases to select the critical points of a digitized curve such that the deviation, from the digitized curve to its final approximated curve, is bounded by a uniform error tolerance. The time complexity of this algorithm is O(m/sup 2/) rather than O(n/sup 2/) on the theoretical plane. In the experiments of fixing the initial and the final processing points, the performance of the algorithm has been compared to those of three prominent other algorithms regarding the required number of critical points and the total execution time of the program. Of the four algorithms compared, the present algorithm consistently has the shortest execution time of the program, and it tends most to require as few critical points as the optimum algorithm that was tested.

关键词： piecewise linear approximation approximation algorithms Iterative algorithms piecewise linear techniques linear approximation Iterative methods Image processing Shape Pattern analysis Pattern classification INSPEC: Controlled Indexing computerised picture processing computational complexity INSPEC: Non-Controlled Indexing critical points 2D digitised curves computerised picture processing adaptive reduction piecewise linear approximation square grid time complexity

来源：评论

学校读者我要写书评

暂无评论

引用

EXPERT SYSTEMS WITH APPLICATIONS 2015年第21期42卷 7664-7675页

作者： Banko, Zoltan Abonyi, Janos Univ Pannonia Dept Proc Engn H-8200 Veszprem Hungary

In recent years, expert systems built around time series-based methods have been enthusiastically adopted in engineering applications, thanks to their ease of use and effectiveness. This effectiveness depends on how precisely the raw data can be approximated and how precisely these approximations can be compared. When performance of a time series-based system needs to be improved, it is desirable to consider other time series representations and comparison methods. The approximation, however, is often generated by a non-replaceable element and eventually the only way to find a more advanced comparison method is either by creating a new dissimilarity measure or by improving the existing one further. In this paper, it is shown how a mixture of different comparison methods can be utilized to improve the effectiveness of a system without modifying the time series representation itself. For this purpose, a novel, mixed comparison method is presented for the widely used piecewise linear approximation (PLA), called mixed dissimilarity measure for PLA (MDPLA). It combines one of the most popular dissimilarity measure that utilizes the means of PLA segments and the authors' previously presented approach that replaces the mean of a segment with its slope. On the basis of empirical studies three advantages of such combined dissimilarity measures are presented. First, it is shown that the mixture ensures that MDPLA outperforms the most popular dissimilarity measures created for PLA segments. Moreover, in many cases, MDPLA provides results that makes the application of dynamic time warping (DTW) unnecessary, yielding improvement not only in accuracy but also in speed. Finally, it is demonstrated that a mixed measure, such as MDPLA, shortens the warping path of DTW and thus helps to avoid pathological warpings, i.e. the unwanted alignments of DTW. This way, DTW can be applied without penalizing or constraining the warping path itself while the chance of the unwanted alignments ar

关键词： Dynamic time warping Local distance piecewise linear approximation Similarity Constraining

来源：评论

学校读者我要写书评

暂无评论

Gait Phase Partitioning and Footprint Detection Using Mutually Constrained piecewise linear approximation with Dynamic Programming

引用

IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 2021年第11期E104D卷 1951-1962页

作者： Yasukawa, Makoto Makihara, Yasushi Hosoi, Toshinori Kubo, Masahiro Yagi, Yasushi Osaka Univ Ibaraki 5670047 Japan NEC Corp Ltd Kawasaki Kanagawa 2118666 Japan

Human gait analysis has been widely used in medical and health fields. It is essential to extract spatio-temporal gait features (e.g., single support duration, step length, and toe angle) by partitioning the gait phase and estimating the footprint position/orientation in such fields. Therefore, we propose a method to partition the gait phase given a foot position sequence using mutually constrained piecewise linear approximation with dynamic programming, which not only represents normal gait well but also pathological gait without training data. We also propose a method to detect footprints by accumulating toe edges on the floor plane during stance phases, which enables us to detect footprints more clearly than a conventional method. Finally, we extract four spatial/temporal gait parameters for accuracy evaluation: single support duration, double support duration, toe angle, and step length. We conducted experiments to validate the proposed method using two types of gait patterns, that is, healthy and mimicked hemiplegic gait, from 10 subjects. We confirmed that the proposed method could estimate the spatial/temporal gait parameters more accurately than a conventional skeleton-based method regardless of the gait pattern.

关键词： gait phase partitioning piecewise linear approximation dynamic programming footprint detection rehabilitation

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：