This paper derives a bisection algorithm for computing the frequency response gain of sampled-data systems with their intersample behavior taken into account. The properties of the infinite-dimensional congruent trans...
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This paper derives a bisection algorithm for computing the frequency response gain of sampled-data systems with their intersample behavior taken into account. The properties of the infinite-dimensional congruent transformation (i.e., the Schur complement arguments and the Sylvester law of inertia) play a key role in the derivation. Specifically, it is highlighted that counting up the numbers of the negative eigenvalues of self-adjoint operators is quite important for the computation of the frequency response gain. This contrasts with the well-known arguments on the related issue of the sampled-data H-infinity problem, where the key role is played by the positivity of operators and the loop-shifting technique. The effectiveness of the derived algorithm is demonstrated through a numerical example.
In this paper, we compute H. -norm of a transfer matrix, via bisection algorithm. The algorithm is given and applied some problems. The problems are choosen from various areas of control theory such as aircraft models...
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In this paper, we compute H. -norm of a transfer matrix, via bisection algorithm. The algorithm is given and applied some problems. The problems are choosen from various areas of control theory such as aircraft models and decentralized interconnected systems.
The finite element method usually requires regular or strongly regular families of partitions in order to get guaranteed a priori or a posteriori error estimates. In this paper we examine the recently invented longest...
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The finite element method usually requires regular or strongly regular families of partitions in order to get guaranteed a priori or a posteriori error estimates. In this paper we examine the recently invented longest-edge bisection algorithm that always produces only face-to-face simplicial partitions. First, we prove that the regularity of the family of partitions generated by this algorithm is equivalent to its strong regularity in any dimension. Second, we present a number of 3d numerical tests, which demonstrate that the technique seems to produce regular (and therefore strongly regular) families of tetrahedral partitions. However, a mathematical proof of this statement is still an open problem. (C) 2013 Elsevier B.V. All rights reserved.
In this paper, we propose a novel cross-range scaling technique to estimate the rotational velocity (RV) of a maneuvering target. The proposed method includes three steps. First, a feature from accelerated segment tes...
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In this paper, we propose a novel cross-range scaling technique to estimate the rotational velocity (RV) of a maneuvering target. The proposed method includes three steps. First, a feature from accelerated segment test (FAST) is applied to two sequential inverse synthetic aperture radar (ISAR) images to find the locations of their robust feature points. Second, the rotation angle (RA) is estimated using two major axes, which are obtained using a principal component analysis (PCA) of the two feature data sets scaled by a candidate RV. Third, an RV search operation based on the measured RA is carried out via the bisection algorithm, which optimizes a newly devised cost function. Compared with the conventional method, the proposed method has two main advantages: 1) it requires no information about the rotation center of a target, and 2) it can efficiently generate a well-scaled ISAR image within a very short time. Finally, the results of experiments using point scatterers and real flying aircraft are provided to demonstrate the validity of the proposed method.
The purpose of this letter is the introduction of a novel methodology for expedited multiobjective design of antenna structures. The key component of the presented approach is fast identification of the initial repres...
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The purpose of this letter is the introduction of a novel methodology for expedited multiobjective design of antenna structures. The key component of the presented approach is fast identification of the initial representation of the Pareto front (i.e., a set of design representing the best possible tradeoffs between conflicting objectives) using a Pareto-ranking bisection algorithm. The algorithm finds a discrete set of Pareto-optimal designs. Its operation principle is sequential partitioning of the line segments connecting the designs found in the previous iterations, and refining the new designs allocated this way by means of poll-type search involving Pareto ranking. Subsequently, the final Pareto set is obtained by means of response correction techniques. Our methodology is demonstrated using an ultrawideband monopole antenna and compared to state-of-the-art multiobjective optimization methods.
In this paper, a novel technique for fast multi-objective design optimization of antenna structures has been presented. In our approach, the initial approximation of the Pareto front is obtained using a bisection algo...
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ISBN:
(纸本)9781509048373
In this paper, a novel technique for fast multi-objective design optimization of antenna structures has been presented. In our approach, the initial approximation of the Pareto front is obtained using a bisection algorithm which performs sequential partitioning of the design space and refines the new designs by means of poll-type search involving Pareto ranking. This stage of the optimization process is executed at the level of low-fidelity EM antenna model. The final Pareto set is found using surrogate-assisted techniques. The approach is demonstrated using a UWB monopole antenna.
A deterministic technique for fast surrogate-assisted multi-objective design optimization of antennas in highly-dimensional parameters spaces has been discussed. In this two-stage approach, the initial approximation o...
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A deterministic technique for fast surrogate-assisted multi-objective design optimization of antennas in highly-dimensional parameters spaces has been discussed. In this two-stage approach, the initial approximation of the Pareto set representing the best compromise between conflicting objectives is obtained using a bisection algorithm which finds new Pareto-optimal designs by dividing the line segments interconnecting previously found optimal points, and executing poll-type search that involves Pareto ranking The initial Pareto front is generated at the level of the coarsely-discretized EM model of the antenna. In the second stage of the algorithm, the high-fidelity Pareto designs are obtained through optimization of corrected local-approximation models. The considered optimization method is verified using a 17-variable uniplanar antenna operating in ultra-wideband frequency range. The method is compared to three state-of-the-art surrogate-assisted multi-objective optimization algorithms. (C) 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the International Conference on Computational Science
Programming-based activities are becoming more widespread in curricula. Our theoretical and empirical investigation seeks to identify appropriate ways to connect computer programming and algorithmics to mathematical l...
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Programming-based activities are becoming more widespread in curricula. Our theoretical and empirical investigation seeks to identify appropriate ways to connect computer programming and algorithmics to mathematical learning. We take the intermediate value theorem as our starting point, as it is covered by the French school curriculum, and because of its links with the bisection algorithm. We build upon the theory of mathematical working spaces, distinguishing between algorithmic and mathematical working spaces. Both working spaces are explored from the semiotic, instrumental, and discursive dimensions that support learning. Our two research questions focus on the suitable algorithmic and mathematical working spaces in which students develop an understanding of the intermediate value theorem, and the bisection algorithm. Our method starts at the reference level, with an epistemological and curricular analysis. Then, a series of tasks is designed for students working in adidacticity, and suitable working spaces are determined a priori. The tasks have been implemented in French classrooms with students aged 16-19. An analysis of their work supports an a posteriori examination of the working spaces. Our findings demonstrate that the students were able to make connections between algorithmics and mathematics in each of the three dimensions, semiotic, instrumental, and discursive, and point out the interplay between these dimensions.
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