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A hybrid quantum-spectral-successive linearization method for general Lane-Emden type equations

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2025年第2期71卷 1581-1607页

作者： Abbasbandy, Saeid Imam Khomeini Int Univ Fac Sci Dept Appl Math Qazvin Iran

This article presents a novel approach for solving the general Lane-Emden type equation with the quantum spectral method. This equation is a nonlinear initial value problem. We use a successive linearization to convert our problem to a linear system of equations, which is solved by a simple iteration method. This method is an iterative algorithm by combining quantum computing, pseudo-spectral, and successive linearization methods. In each iteration, we used a quantum algorithm and the final quantum state can be obtained by adding the quantum state in each iteration. Some numerical examples are considered and comparison with other existing methods, shows the efficiency of the method.

关键词： Quantum method Spectral method linearization method Lane-Emden equations Lane-Emden-Fowler equations

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A linearization method for the transverse-leakage terms in hexagonal nodal method based on the conformal mapping technique

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ANNALS OF NUCLEAR ENERGY 2025年 217卷

作者： Wan, Chenghui Yang, Haozhe Bai, Jiahe Zhang, Jianfu Wang, Songzhe Shen, Wei Xi An Jiao Tong Univ Sch Nucl Sci & Technol Xian Peoples R China Jiangsu Nucl Power Corp Lianyungang Peoples R China

Widely used in the hexagonal-assembly core-analysis code, the conformal mapping technique has proved to be suitable, accurate, and efficient. Throughout the years of its fledging development, there was hardly any treatment generally applicable for the conformally mapped transverse-leakage terms. This issue notably affected the calculation accuracy of the hexagonal nodal calculation. To address this issue, in the present study, a linearization method for the transverse-leakage terms has been proposed, which estimates the current distribution of nodal surfaces with corresponding flux distribution on surfaces adjacent to neighboring nodes. This method provides an accurate distribution of the transverse-leakage terms, leading to calculation results with high accuracy. The proposed method has been implemented in our in-house core-analysis code, SPARK, enabling the solution of the three-dimensional multi-group neutron-diffusion equation using hexagonal nodes. To verify the method, the two-dimensional VVER-1000 benchmark problem was calculated in the first place. Compared with the conventional flat-current assumption, the proposed linearization method decreased the error of eigenvalue and the maximum error of the nodal normalized power from 62.9 pcm to 8.6 pcm and from 5.60% to -0.65%, respectively. Subsequently, numerous 2D/3D benchmarks were modeled and verified, comparing the eigenvalues and assembly-averaged power distributions with their corresponding reference values. The numerical results indicate that the proposed linearization method performs satisfactorily, reducing the maximum error in eigenvalue to about 20.0 pcm and keeping the errors in power distribution below 0.9%. As a result, the proposed linearization method significantly improves computation accuracy and offers an effective solution for handling the transverse-leakage terms using the conformal mapping technique.

关键词： Transverse-leakage term Conformal mapping technique Hexagonal-assembly core linearization method

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Exponential stability analysis of switched nonlinear systems: A linearization method

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AUTOMATICA 2024年 163卷

作者： Liu, Xingwen Chen, Zumei Shi, Kaibo Li, Min Zhong, Shouming Southwest Minzu Univ Coll Elect Engn Ctr Intelligent Complex Syst Chengdu 610225 Sichuan Peoples R China Chengdu Univ Sch Elect Informat & Elect Engn Chengdu 610106 Sichuan Peoples R China Univ Elect Sci & Technol China Sch Math Sci Chengdu 611731 Sichuan Peoples R China

This paper addresses the exponential stability issue of discrete -time switched nonlinear systems by means of the linearization approach. Generally speaking, the linearization method requires that the vector field of the original nonlinear system is continuously differentiable. Since the vector field of a switched system does not meet the differentiable condition (discontinuous at switching instants), the linearization method is seldom used in the context of switched systems. In the present paper, it is assumed that the vector field of each subsystem is continuously differentiable. With this assumption, two Lyapunov theorems are proposed to verify the exponential and asymptotic stabilities of the considered system. Applying these results and using the linearized system, a multiple homogeneous polynomial Lyapunov function (HPLF) is adapted to establish the exponential stability of switched nonlinear systems. Moreover, it is shown that the conservatism of the stability condition reduces as the degree of the HPLF increases. (c) 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： Arbitrary switchings Asymptotic stability Exponential stability linearization method Switched nonlinear systems

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linearization method for Optimizing Noncoplanar Flights with Low Thrust

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SOLAR SYSTEM RESEARCH 2020年第7期54卷 699-706页

作者： Vernigora, L. V. Kazmerchuk, P. V. Lavochkin Assoc Chimki 141400 Moscow Oblast Russia

Problems on optimizing the noncoplanar flights with low thrust from elliptical to geosynchronous orbits for different control accelerations are solved. Recommendations for choosing an initial approximation are given. ... 详细信息

关键词： linearization method low thrust nonlinear optimization

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Application of a novel linearization method to compare the on-off control strategies modeled by piecewise linear systems

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JOURNAL OF VIBRATION AND CONTROL 2020年第23-24期26卷 2125-2135页

作者： Sireteanu, Tudor Solomon, Ovidiu Mitu, Ana-Maria Giuclea, Marius Romanian Acad Inst Solid Mech 15 Ctin Mille St Bucharest 010071 Romania Bucharest Univ Econ Studies Dept Appl Math Bucharest Romania

In this study, a novel approach for linearization of piecewise linear systems is applied to approximate the root mean square output of a quarter car model with semiactive control. The on-off control strategies, balance logic, skyhook, groundhook, and hybrid are modeled by piecewise linear systems with variable friction. By the proposed method, one can attach, for each output of practical interest, a linear system with the same transmissibility factor. The obtained transmissibility factors are used to approximate the root mean square output of considered semiactive systems using the power spectral density input-output relationships for constant parameter linear systems with stationary random inputs. The method is applied for optimization of hybrid control strategy with respect to a performance index defined in terms of sprung mass acceleration, suspension travel, and dynamic contact force.

关键词： Piecewise linear systems linearization method transmissibility factors semiactive control strategies suspension optimization

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A linearization method in the “Attack–Defense” Game with Nonhomogeneous Opponent Resources

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Computational Mathematics and Modeling 2020年第1期31卷 104-115页

作者： Perevozchikov, A.G. Reshetov, V. Yu Yanochkin, I.E. Research and Production Association “Rusbitech” Tver Russian Federation Lomonosov Moscow State University Moscow Russian Federation Research and Production Association “Rusbitech” Tver Russian Federation

A nonhomogeneous generalization of the “attack–defense” game is considered. A linearization method is proposed to determine the best guaranteed outcome (BGO) of defense. The linearization utilizes a decomposition of the solution in a small parameter in the neighborhood of the trivial uniform distribution of defense resources. We show that the determination of correcting perturbations to the trivial uniform allocation of defense resources is reducible to a linear program. A prototype example to construct the correcting perturbations is considered. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

关键词： best guaranteed outcome of defense classical “attack–defense” game decomposition of the solution in a small parameter linearization method nonhomogeneous generalization

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linearization method for Solving Quantile Optimization Problems with Loss Function Depending on a Vector of Small Random Parameters

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AUTOMATION AND REMOTE CONTROL 2017年第7期78卷 1251-1263页

作者： Vasil'eva, S. N. Kan, Yu. S. Natl Res Univ Moscow Aviat Inst Moscow Russia

We propose a method for solving quantile optimization problems with a loss function that depends on a vector of small random parameters. This method is based on using a model linearized with respect to the random vector instead of the original nonlinear loss function. We show that in first approximation, the quantile optimization problem reduces to a minimax problem where the uncertainty set is a kernel of a probability measure.

关键词： quantile optimization linearization method vector of small random parameters kernel of a probability measure

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A linearization method of Piecewise Linear Systems Based on Frequency Domain Characteristics With Application to Semi-Active Control of Vibration

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JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME 2018年第6期140卷 061006-061006页

作者： Sireteanu, Tudor Solomon, Ovidiu Mitu, Ana-Maria Giuclea, Marius Romanian Acad Inst Solid Mech 15 Constantin Mille Bucharest 010141 Romania Bucharest Univ Econ Studies Dept Appl Math 6 Romana Sq Bucharest 010374 Romania

In this paper, a new approach is presented for linearization of piecewise linear systems with variable dry friction, proportional with absolute value of relative displacement. The transmissibility factors of considered systems, defined in terms of root-mean-square (RMS) values, are obtained by numerical time integration of motion equations for a set of harmonic inputs with constant amplitude and different frequencies. A first-order linear differential system is attached to the considered piecewise linear system such as the first component of solution vector of attached system to have the same transmissibility factor as the chosen output of nonlinear system. This method is applied for the semi-active control of vibration with balance logic strategy. Applications to base isolation of rotating machines and vehicle suspensions illustrate the effectiveness of the proposed linearization method.

关键词： piecewise linear systems variable dry friction semi-active control transmissibility factors linearization method

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linearization method of Voltage Gain for VSI-PWM in Overmodulation Area 16

Linearization Method of Voltage Gain for VSI-PWM in Overmodu...

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16th International Conference of Young Specialists on Micro/Nanotechnologies and Electron Devices

作者： Bakhovtsev, Igor A. Mednya, Vladislav G. Novosibirsk State Tech Univ Novosibirsk Russia

ISBN: (纸本)9781467367196

In paper is considered the problem of the extension of linear control range of output voltage of VSI-PWM due to use of overmodulation area. linearization method of the voltage gain in the all range up to the six-step mode is offered. Comparing of the offered method with a method pulse-width control on quality of output voltage is carried out.

关键词： VSI PWM voltage gain linearization method overmodulation area

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The method of linearization in Optimization Problems of Low-Thrust Spacecraft Trajectories: Optimal Nodes Layout

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SOLAR SYSTEM RESEARCH 2022年第7期56卷 521-526页

作者： Kazmerchuk, P. V. Vernigora, L. V. Lavochkin Assoc Chimki Moscow oblast Russia

The paper considers the possibility of joint optimization of the control of a low-thrust spacecraft and the layout of nodes approximating the control function using a modified linearization method.

关键词： linearization method low thrust linear optimization

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