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Investigation of Selected Reconstruction algorithms Used for Determination of Complex Ratio of AC Voltages

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2021年 70卷 1页

作者： Augustyn, Jerzy Kampik, Marian Musiol, Krzysztof Kielce Univ Technol Dept Comp Sci Elect & Elect Engn PL-25314 Kielce Poland Silesian Tech Univ Dept Measurement Sci Elect & Control PL-44100 Gliwice Poland

Issues related to measurements of the complex ratio of two sinusoidal voltages based on digital sampling are considered in this article. Several algorithms for determination of the complex voltage ratio are discussed. Results of five algorithms are compared and minimizing their errors related to differences between the two sampling channels is examined. For verification, a sampling system with National Instruments PXI 4461 data acquisition module (DAQm) was used.

关键词： Channel swapping complex voltage ratio (CVR) data acquisition (DAQ) channel errors discrete Fourier transform (DFT) ellipse fitting (EF) numerical algorithms sampling sine-fitting (SF)

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An Adaptive Local Variational Iteration Method for Orbit Propagation and Strongly Nonlinear Dynamical Systems

An Adaptive Local Variational Iteration Method for Orbit Pro...

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AIAA Science and Technology Forum and Exposition (AIAA SciTech)

作者： Wang, Xuechuan Elgohary, Tarek A. Atluri, Satya N. Northwestern Polytech Univ Sch Astronaut Xian Peoples R China Univ Cent Florida Dept Mech & Aerosp Engn Orlando FL 32816 USA Texas Tech Univ Dept Mech Engn Lubbock TX 79415 USA

ISBN: (数字)9781624105951

ISBN: (纸本)9781624105951

In this paper, a very simple and efficient Adaptive Local Variational Iteration Method (LVIM) for solving problems of nonlinear dynamics and orbital mechanics is presented. The analytical iteration formula of this method is derived by using a general form of first order nonlinear differential equations, followed by straightforward discretization using Chebyshev polynomials and collocation. The resulting numerical algorithm is very concise and easy to use, only involving highly sparse matrix operations of addition and multiplication, and no inversion of the Jacobian is required. Apart from the simple yet efficient iteration formula, a straightforward adaptive scheme is introduced to refine the step size and the collocation nodes at each time segment. The proposed adaptive method guarantees the prescribed accuracy without needing to manually tune the algorithm. It also prevents over-calculating in the computational process by relaxing the refinement automatically. numerical results of large amplitude pendulum and the perturbed two-body problem validate the high accuracy and efficiency of this easy-to-use adaptive method.

关键词： Orbital Mechanics numerical algorithms Nonlinear Dynamics Predictor Corrector Method MATLAB Perigee High Performance Computing Runge Kutta Methods Nonlinear Systems Earth

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On Determination of Complex Ratio of AC Voltages in a Simultaneously Sampled Two-Channel Data Acquisition System

On Determination of Complex Ratio of AC Voltages in a Simult...

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Joint Conference of Conference on Precision Electromagnetic Measurements (CPEM) and Conference of NCSL-International (NCSLI)

作者： Augustyn, Jerzy Kampik, Marian Musiol, Krzysztof Kielce Univ Technol Kielce Poland Silesian Tech Univ Gliwice Poland

ISBN: (数字)9781728158983

ISBN: (纸本)9781728158983

The article presents the results of measurements of the complex ratio of two sinusoidal voltages (CVR) implemented using PXI system with the National Instrument (NI) PXI 4461 data acquisition module, simultaneously sampling sinusoidal voltages. Results of three reconstruction algorithms were compared and the possibility of minimizing errors related to difference between 4461 module channels was examined.

关键词： complex voltage ratio sampling numerical algorithms DFT sine-fitting ellipse fitting phase shift

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A GPU-Accelerated Barycentric Lagrange Treecode 34

A GPU-Accelerated Barycentric Lagrange Treecode

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34th IEEE International Parallel and Distributed Processing Symposium (IPDPS)

作者： Vaughn, Nathan Wilson, Leighton Krasny, Robert Univ Michigan Dept Math Ann Arbor MI 48109 USA

ISBN: (数字)9781728174457

ISBN: (纸本)9781728174457

We present an MPI + OpenACC implementation of the kernel-independent barycentric Lagrange treecode (BLTC) for fast summation of particle interactions on GPUs. The distributed memory parallelization uses recursive coordinate bisection for domain decomposition and MPI remote memory access to build locally essential trees on each rank. The particle interactions are organized into target batch/source cluster interactions which efficiently map onto the GPU;target batching provides an outer level of parallelism, while the direct sum form of the barycentric particle-cluster approximation provides an inner level of parallelism. The GPU-accelerated BLTC performance is demonstrated on several test cases up to 1 billion particles interacting via the Coulomb potential and Yukawa potential.

关键词： Heterogeneous (hybrid) systems Graphics processors Load balancing and task assignment Interpolation numerical algorithms Parallel algorithms Chebyshev approximation and theory Integral Equations

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Relativistic Maxwellian mixture model

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PHYSICS OF PLASMAS 2021年第12期28卷 122106-122106页

作者： Ueno, Genta Zenitani, Seiji Inst Stat Math 10-3 Midori Cho Tokyo 1908562 Japan Kobe Univ Res Ctr Urban Safety & Secur Nada Ku 1-1 Rokkodai Cho Kobe Hyogo 6578501 Japan

For analyzing distribution functions of relativistic plasma, we propose a mixture model composed of relativistic Maxwellian distributions. We first summarize the basic properties of the relativistic Maxwellian distribution, including the derivation of the normalization constant when there is a bulk velocity. We also examine the maximum likelihood estimation of the relativistic Maxwellian distribution. We then introduce a relativistic Maxwellian mixture model (R-MMM), which is a weighted sum of relativistic Maxwellian distributions. We develop an expectation-maximization algorithm for estimating the parameters of R-MMM, namely, the mixing proportion, the bulk velocity, and the temperature of each component. We apply a two-component R-MMM to a distribution function by a particle-in-cell (PIC) simulation of relativistic pair plasma and separate the simulated distribution function into two components. We find that one component has a large bulk velocity while the other is almost stagnant, and that the two components have almost the same temperatures, which is also consistent with the initial temperature of PIC simulation. (c) 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http:// ***/licenses/by/4.0/). https://***/10.1063/5.0059126

关键词： Topics: Maxwell-Boltzmann distribution Special relativity Nonequilibrium statistical mechanics Relativistic effects Statistical models Particle-in-cell method numerical algorithms Magnetic reconnection EM algorithm Particle distribution functions.

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Robust Stackelberg Games via Static Output Feedback Strategy for Uncertain Stochastic Systems with State Delay 21st

Robust Stackelberg Games via Static Output Feedback Strategy...

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21st IFAC World Congress on Automatic Control - Meeting Societal Challenges

作者： Mukaidani, Hiroaki Ramasamy, Saravanakumar Xu, Hua Zhuang, Weihua Hiroshima Univ 1-7-1 Kagamiyama Higashihiroshima 7398521 Japan Univ Tsukuba Bunkyo Ku 3-29-1 Otsuka Tokyo 1120012 Japan Univ Waterloo 200 Univ Ave West Waterloo ON N2L 3G1 Canada

In this paper, a robust Stackelberg game for a class of uncertain stochastic systems with state delay is investigated. After introducing some definitions and preliminaries, we derive the conditions for the existence of the robust static output feedback (SOF) Stackelberg strategy set such that the upper bounds of leader's cost function and the weighted cost function of the followers are minimized respectively. In order to obtain the robust SOF Stackelberg strategy set, a heuristic algorithm is proposed based on the stochastic Lyapunov type matrix equations (SLMEs) and the linear matrix inequalities (LMIs). In particular, it is shown that robust convergence is guaranteed by applying the Krasnoselskii-Mann (KM) iterative algorithm. An academic numerical example is presented to demonstrate the effectiveness of the proposed method. Copyright (C) 2020 The Authors.

关键词： Stackelberg games H-infinity control stochastic systems numerical algorithms

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First-Order Methods for Convex Optimization

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EURO JOURNAL ON COMPUTATIONAL OPTIMIZATION 2021年 9卷

作者： Dvurechensky, Pavel Shtern, Shimrit Staudigl, Mathias Weierstrass Inst Appl Anal & Stochast Mohrenstr 39 D-10117 Berlin Germany Inst Informat Transmiss Problems RAS Bolshoy Karetny Per 19Build 1 Moscow 127051 Russia Moscow Inst Phys & Technol 9 Inst Skiy Per Dolgoprudnyi 141701 Moscow Region Russia Technion Israel Inst Technol Fac Ind Engn & Management Haifa Israel Maastricht Univ Dept Data Sci & Knowledge Engn DKE Paul Henri Spaaklaan 1 NL-6229 EN Maastricht Netherlands Maastricht Univ Math Ctr Maastricht MCM Paul Henri Spaaklaan 1 NL-6229 EN Maastricht Netherlands

First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories reported in various applications, including most importantly machine learning, signal processing, imaging and control theory. First-order methods have the potential to provide low accuracy solutions at low computational complexity which makes them an attractive set of tools in large-scale optimization problems. In this survey, we cover a number of key developments in gradient-based optimization methods. This includes non-Euclidean extensions of the classical proximal gradient method, and its accelerated versions. Additionally we survey recent developments within the class of projection-free methods, and proximal versions of primal dual schemes. We give complete proofs for various key results, and highlight the unifying aspects of several optimization algorithms.

关键词： Convex Optimization Composite Optimization First-Order Methods numerical algorithms Convergence Rate Proximal Mapping Proximity Operator Bregman Divergence

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Extension of Unified Trigonometrization Method to Enforce Inequality Boundary Conditions in Optimal Control Problems

Extension of Unified Trigonometrization Method to Enforce In...

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AIAA Aviation Forum

作者： Nolan, Sean M. Sparapany, Michael J. DeLaurentis, Daniel Purdue Univ Aeronaut & Astronaut Engn W Lafayette IN 47904 USA

ISBN: (数字)9781624105982

ISBN: (纸本)9781624105982

Solving optimal control problems with indirect methods is historically challenging, especially when problems contain complex features such as inequality constraints. For this reason in large part, direct methods have dominated trajectory optimization since the advent of sufficiently fast digital computers. Recently though, new methods and techniques have arisen to make indirect methods more accessible and reliable thus enabling the generation of high-quality solutions. One of these methods, the Unified Trigonometrization Method, aids solving problems with inequality path constraints on states and controls by modifying the optimal control problem. The work presented here extends the Unified Trigonometrization Method to handle inequality constraints on the initial and terminal boundaries as well. It does so by augmenting the initial and terminal cost with two-sided interior penalty functions mirroring the original method's handling of state path constraints. A variation of Zermelo's navigation problem verifies and illustrates the method, and a Space Shuttle re-entry problem demonstrates the new method's efficacy and applicability for more complex aerospace problems.

关键词： Zermelo's Navigation Problem Space Shuttle Digital Computers Flight Path Angle Terminal Velocity Nonlinear Programming Lagrange Multipliers Boundary Value Problems Angle of Attack numerical algorithms

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Robust Incentive Stackelberg Strategy for Markov Jump Delay Stochastic Systems via Static Output Feedback 21st

Robust Incentive Stackelberg Strategy for Markov Jump Delay ...

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21st IFAC World Congress on Automatic Control - Meeting Societal Challenges

A static output feedback (SOF) incentive Stackelberg game (ISG) for a continuous-time Markov jump delay stochastic system (MJDSS) is discussed. The existence conditions on the SOF incentive Stackelberg strategy set are established in terms of the solvability of a set of higher-order cross-coupled stochastic algebraic Lyapunov-type equations (CCSALTEs). A classical Lagrange-multiplier technique is used to derive the CCSALTEs, thereby avoiding having to solve the bilinear matrix inequalities (BMIs), a well-known NP-hard problem in designing the SOF strategy. A heuristic algorithm is proposed to solve CCSALTEs such that convergence is attained by applying the Krasnoselskii-Mann (KM) iterative algorithm. A simple numerical example demonstrates the efficiency of the SOF incentive Stackelberg strategy. Copyright (C) 2020 The Authors.

关键词： Stackelberg games H-infinity control stochastic systems numerical algorithms

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A Column Space Based Approach to Solve Systems of Multivariate Polynomial Equations ⁎ ⁎

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IFAC-PapersOnLine 2021年第9期54卷 137-144页

作者： Christof Vermeersch Bart De Moor Center for Dynamical Systems Signal Processing and Data Analytics (STADIUS) Dept. of Electrical Engineering (ESAT) KU Leuven Kasteelpark Arenberg 10 3001 Leuven Belgium

We propose a novel approach to solve systems of multivariate polynomial equations, using the column space of the Macaulay matrix that is constructed from the coefficients of these polynomials. A multidimensional realization problem in the null space of the Macaulay matrix results in an eigenvalue problem, the eigenvalues and eigenvectors of which yield the common roots of the system. Since this null space based algorithm uses well-established numerical linear algebra tools, like the singular value and eigenvalue decomposition, it finds the solutions within machine precision. In this paper, on the other hand, we determine a complementary approach to solve systems of multivariate polynomial equations, which considers the column space of the Macaulay matrix instead of its null space. This approach works directly on the data in the Macaulay matrix, which is sparse and structured. We provide a numerical example to illustrate our new approach and to compare it with the existing null space based root-finding algorithm.

关键词： Macaulay matrix multivariate polynomials numerical algorithms realization theory matrix algebra

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