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Accurate Calculation of the Settling Time of a Linear System Using New Expressions and iterative algorithms

CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2018年第1期37卷 408-431页

作者： Chagra, Wassila Univ Tunis El Manar Lab Analyse Conception & Commande Syst Inst Preparatoire Etud Ingn El Manar LR11ES20Ecole Natl Ingn Tunis BP 37 Tunis 1002 Tunisia

The purpose of this paper is to achieve an exhaustive and generalized method for the accurate calculation of the linear system settling time. Thus, the classical settling time expressions for the second-order linear systems are reviewed. Then, new expressions are proposed and developed for the step response of the second-order and for higher-order under-damped and over-damped linear systems. The proposed expressions are different from all the existing ones, and they are more accurate. In addition, iterative algorithms that can be easily implemented are proposed in order to achieve accurate calculation of the settling time. The accuracy of the new expressions and the proposed iterative algorithms are illustrated by several numerical simulation examples.

关键词： Settling time Accurate calculation Fixed point method iterative algorithm Higher-order linear systems

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High-Performance Blind Spectrum Sensing: An iterative Unsupervised Learning Approach 5

High-Performance Blind Spectrum Sensing: An Iterative Unsupe...

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5th International Conference on Information Science, Computer Technology and Transportation (ISCTT)

作者： Gao, Shishun Zhao, Haitao Zhang, Jiao Wang, Haijun Wei, Jibo Natl Univ Def Technol Coll Elect Sci Changsha 410073 Peoples R China

ISBN: (纸本)9781728185750

In the research of blind spectrum sensing, unsupervised learning has been regarded as a promising technology to detect spectrum status without any prior knowledge or labeled signals. However, the detection performance of the existing unsupervised sensing methods is usually far below that of supervised sensing methods. In order to overcome this problem, we propose an iterative unsupervised learning based cooperative spectrum sensing (CSS) algorithm, where the concept of iteration is introduced to improve detection performance. Specifically, in each iteration, i) The CSS technology is first used to make global labels by combining the local labels of the individual detectors constructed in the last iteration;ii) And then, individual detectors are constructed by utilizing supervised learning to fit the mapping from local sample set to the current global labels. During above iterative process, the global labels contribute to improving individual detectors, while these improved individual detectors can cooperatively make more accurate global labels, which will be utilized in next iteration. Finally, with the increase of the number of iterations, these individual detectors can be used to online cooperatively detect spectrum status when there are only slight changes in global labels. Simulation results show that the proposed algorithm can achieve comparable individual and cooperative detection performance with the existing supervised sensing methods over a wide signal-to-noise ratio (SNR) region.

关键词： Cooperative spectrum sensing unsupervised learning iterative algorithm cognitive radio

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Reducing the Noise Impact of Small Aircraft through Indirect Trajectory Optimization

Reducing the Noise Impact of Small Aircraft through Indirect...

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AIAA Aviation Forum

作者： Galles, Matthew B. Newman, Brett NASA Langley Res Ctr Struct Acoust Branch MS 463 Hampton VA 23681 USA Old Dominion Univ Dept Mech & Aerosp Engn Norfolk VA 23529 USA

ISBN: (数字)9781624105982

ISBN: (纸本)9781624105982

This research examined the feasibility of incorporating an acoustic metric into the optimization of an aircraft trajectory to reduce the noise experienced by an observer. The method investigated a perturbed path of an unmanned aerial system with specified boundary conditions on position and velocity while maintaining a nominal flight speed. An acoustic model based on Gutin's work was developed to estimate propeller noise as a function of flight parameters, propulsion characteristics, and spatial location. A trajectory was then optimized a priori to reduce the noise experienced by an observer. Multiple simulations were performed and results showed that integrating an acoustic metric into the path planning process could be used to reduce the noise impact on an observer with no perturbation to the nominal flight speed.

关键词： Pontryagin's Maximum Principle Aircrafts Propeller Noise Real Time Path Planning Aircraft Trajectory Unmanned Aerial Systems Overall Sound Pressure Level Flight Control System iterative algorithm Flight Trajectory

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A nonlinear subiteration strategy for improved robustness of pseudo-transient continuation methods

A nonlinear subiteration strategy for improved robustness of...

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AIAA Aviation Forum

作者： Plouviez, Leon Wolff, Eric Wukiet, Nathan A. Schrock, Christopher Def Sci & Technol Lab Grad Dev Scheme Fareham Hants England Ohio Aerosp Inst Dayton OH USA Air Force Res Lab Wright Patterson AFB OH USA Multidisciplinary Sci & Technol Ctr Dayton OH USA

ISBN: (数字)9781624105982

ISBN: (纸本)9781624105982

Newton's method for solving nonlinear systems of equations have historically been augmented with pseudo-transient continuation (PTC) methods as a strategy for constructing a globally convergent nonlinear iterative algorithm. The PTC-Newton algorithm is often combined with other globalisation approaches such as line searches and residual smoothing to improve overall convergence and robustness of the method [1]. In this work a nonlinear subiteration strategy is applied to the steps of the PTC procedure to improve the robustness of the overall nonlinear iterative method. This method is compared against a baseline PTC-Newton algorithm and a residual smoothing procedure proposed by Mavriplis et al. [2]. Two problems are studied in order to quantify differences in robustness and convergence properties between the methods. These problems are: a simulation of subsonic, turbulent flow over a Joukowski aerofoil using the Reynolds-Averaged Navier-Stokes (RANS) equations and a simulation of inviscid, supersonic flow in a ramp channel using the Euler equations with artificial viscosity for shock capturing. Results indicate the subiteration strategy can ameliorate convergence challenges that might traditionally result in backtracking failure or stagnation. The subiteration strategy is shown to converge in cases where both PTC-Newton and residual smoothing methods encounter failure, and this robustness is then leveraged to enable stronger CFL ramping. Significant robustness and efficiency benefits are shown in both cases

关键词： Courant Friedrichs Lewy Reynolds Averaged Navier Stokes Discontinuous Galerkin Method Aerofoil Supersonic Flow Nonlinear Systems Viscosity iterative algorithm Euler Equations Spalart Allmaras Turbulence Model

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V-E algorithm: A New Vital Vertex Identifying algorithm Based on Vertex-Edge Interaction

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2021年第5期38卷 2140013-2140013页

作者： Wang, Haoyu Qi, Xingqin Shandong Univ Sch Math Jinan 250100 Shandong Peoples R China Shandong Univ Sch Math & Stat Weihai 264209 Shandong Peoples R China

Finding vital vertices is an important issue in complex network analysis, which has wide applications in disease control, information diffusion, etc. This topic has attracted increasing attention from various disciplines. In this paper, we propose a new algorithm called Vertex-Edge algorithm to find vital vertices. This algorithm takes both the incident edges and also its neighbors into consideration when evaluating a vertex's importance, and the importance of vertices and edges construct a mutually updated iterative framework. We also give convergence conditions for the iterative framework. Besides, we verify the stability, effectiveness, accuracy, and superiority of this new Vertex-Edge algorithm by applying it on lots of networks (unweighted or weighted) and comparing the results with other 10 more existing methods. This new method is expected to have promising applications in the future.

关键词： Complex networks vital nodes identification centrality measures iterative algorithm

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An iterative scheme for identifying the positive semi-definiteness of even-order real symmetric H-tensor

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2021年 392卷 113498-113498页

作者： Lv, Changqing Ma, Changfeng Fujian Normal Univ Sch Math & Informat Fuzhou 350117 Peoples R China Zaozhuang Univ Sch Math & Stat Zaozhuang 277160 Peoples R China FJKLMAA Fuzhou 350117 Peoples R China Ctr Appl Math Fujian Prov FJNU Fuzhou 350117 Peoples R China

H-tensor plays an important role in identifying the positive (semi-) definiteness of even-order real symmetric tensor. In this paper, we propose an algorithm for identifying general H-tensor and prove the algorithm will terminate within finite iterative steps. As application, we give an iterative method for identifying positive semi-definiteness of the even order symmetric tensor. At last, some numerical examples are provided to illustrate the efficiency and validity of methods we have proposed. (C) 2021 Elsevier B.V. All rights reserved.

关键词： General H-tensor Positive semi-definiteness Generalized diagonal dominance iterative algorithm

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Solving Two Coupled Fuzzy Sylvester Matrix Equations Using iterative Least-squares Solutions

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FUZZY INFORMATION AND ENGINEERING 2020年第4期12卷 464-489页

作者： Bayoumi, Ahmed M. E. Ramadan, Mohamed A. Ain Shams Univ Fac Educ Dept Math Cairo Egypt Menoufia Univ Fac Sci Dept Math Shibin Al Kawm Egypt

In this paper, five iterative methods for solving two coupled fuzzy Sylvester matrix equations are considered. The two coupled fuzzy Sylvester matrix equations are expressed by using the generalized inverse of the coefficient matrix, then iterative solutions are constructed by applying the hierarchical identification principle and by using the block-matrix inner product (the star product for short). A proposed modification to this algorithm to solve the first coupled fuzzy Sylvester matrix equations is suggested. This proposed modification is compared with the first algorithm where our modification exhibits fast convergence behavior. Also, we suggested two least-squares iterative algorithm by applying a hierarchical identification principle to solve the two coupled fuzzy Sylvester matrix equations. The proposed methods are illustrated by numerical examples.

关键词： Coupled fuzzy Sylvester matrix equations iterative algorithm Kronecker product Frobenius norm Star product

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A Fast Analytic Multiple-Sources Angle-of-Arrival Estimation algorithm for Automotive MIMO Radars

A Fast Analytic Multiple-Sources Angle-of-Arrival Estimation...

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IEEE International Symposium on Antennas and Propagation / North American Radio Science Meeting

作者： Cai, Xiuzhang Sarabandi, Kamal Univ Michigan Elect Engn & Comp Sci Dept Ann Arbor MI 48109 USA

ISBN: (纸本)9781728166704

Traditionally, the angle of arrival (AOA) estimation problem for multiple sources is considered as a nonlinear problem with no analytic solutions. In this paper, an analytic iterative multiple-source AOA algorithm (AIMA) is presented for fast and accurate estimation of the AOA. The approach is most useful for automotive MIMO radars where there can be a large number of scatterers in the scene. The AOA estimation problem is divided into two main tasks: (1) estimate one AOA with the prior knowledge of all other AOA;(2) estimate all AOA by iteratively solving Task 1. It can be shown that for a uniform linear array (ULA) Task 1 has analytic solutions and Task 2 converges very fast, which makes this method effective, efficient and practical for real-time processing. Unlike many other AOA estimation methods, this approach doesn't need the information about the number of sources and can be applied for coherent signals and single snapshot as well.

关键词： angle of arrival direction of arrival iterative algorithm

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On Hermitian positive definite solutions of a nonlinear matrix equation

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JOURNAL OF FIXED POINT THEORY AND APPLICATIONS 2021年第2期23卷 30-30页

作者： Masoudi, Mohsen Salemi, Abbas Univ Guilan Fac Math Sci Rasht Iran Shahid Bahonar Univ Kerman Dept Appl Math Kerman Iran Shahid Bahonar Univ Kerman Mahani Math Res Ctr Kerman Iran

In this paper, the Hermitian positive definite solutions of the matrix equation X-s + A* X-t A = Q, where A is an n x n nonsingular complex matrix, Q is an n x n Hermitian positive definite matrix and s, t > 0, are discussed. Some conditions for the existence of Hermitian positive definite solutions of this equation are derived. In addition, two iterative methods to obtaining the maximum or minimum Hermitian positive definite solutions of this equation are proposed. In addition, a necessary and sufficient condition for the existence of these solutions is presented. Theoretical results are illustrated by some numerical examples.

关键词： Nonlinear matrix equation positive definite solution fixed point theorem iterative algorithm

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Weighted multiwindow discrete Gabor transform

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DIGITAL SIGNAL PROCESSING 2021年 117卷 103155-103155页

作者： Li, Rui Kwan, Hon Keung Anhui Sci & Technol Univ Coll Informat & Network Engn Bengbu 233030 Anhui Peoples R China Univ Windsor Dept Elect & Comp Engn Windsor ON N9B 3P4 Canada

According to the Heisenberg uncertainty principle, an analysis window with a high time resolution in time domain will result in a low frequency resolution in frequency domain, and vice versa. To obtain the Gabor spectrum with high time-frequency resolution and concentration, weighted multiwindow discrete Gabor transform (M-DGT) using weights and the biorthogonal analysis method for analyzing long (or infinite) sequences is proposed in this paper, in which the combined Gabor coefficients constructed by a combination of M-DGT coefficients can be adaptively changed according to the time-frequency distributions of an analyzed signal containing multiple time-varying frequencies. To obtain the weights of the weighted M-DGT, the M-DGT is converted into a sparse problem with l(1)-l(2) regularization, then an efficient iterative algorithm for solving the weights in terms of real-valued matrix and real-valued vector is derived. The convergence of the iterative algorithm is proved by optimization theory. The experimental results demonstrate that the proposed method is an effective and efficient tool for nonstationary timefrequency analysis of signals. (C) 2021 Elsevier Inc. All rights reserved.

关键词： Discrete Gabor transform Weighted multiwindow discrete Gabor transform Time-frequency analysis Long and infinite sequences iterative algorithm

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