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第37届中国控制会议

作者： Zhihua Chen Yongchun Xie Beijing Institute of Control Engineering Science and Technology on Space Intelligent Control Laboratory

The paper deals with the uniform finite-time stability(UFTS) of continuous linear time-varying(LTV) ***,a necessary and sufficient condition for the UFTS of continuous LTV systems is devised with the idea of computing the envelope of all the trajectories of the considered ***,a corollary is obtained under the perspective of numerical ***,based on the obtained corollary,a novel numerical algorithm is designed by utilizing the Lipschitz continuity of certain *** the proposed algorithm,only limited numerical computation is needed when analyzing the UFTS of continuous LTV *** with the existing Lyapunov-like function method,one needn't constructing Lyapunov-like ***,the obtained corollary just requires being checked at a limited number of time ***,two numerical examples are provided to illustrate the effectiveness and superiority of the proposed results.

关键词： Linear time-varying system Uniform Finite-time stability numerical algorithm

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Adaptive step size numerical algorithm for fractional order control systems 29

Adaptive step size numerical algorithm for fractional order ...

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第29届中国控制与决策会议

作者： Yongkang He Zhidong Qi Yinyin Tang Di Hu School of automation Nanjing University of Science and Technology

ISBN: (纸本)9781509046584

For fractional order control systems,fast and accurate numerical algorithm is the key step in real-time control and *** the short memory method(SMM) and the constant weight memory method(CWMM)accelerate the computation speed through the choice and approximation of the historical information of the fractional differential operator,the computation precision decreases with the increase of *** CWMM is affected by input function and the error range is *** the limitation of fixed step size discretization(FSSD) of fractional differential operator,a variable step size discretization(VSSD) scheme is *** to the local error obtained by the step-doubling technique,the iterative step size is adjusted *** algorithm not only can achieve good accuracy,uniform error,but also fast calculation speed,which provides a feasible way for the numerical calculation of state space description of fractional order control ***,the reliability of the algorithm is verified by an example.

关键词： Fractional calculus numerical algorithm variable step size discretization adaptive step size

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A numerical algorithm TO INITIAL VALUE PROBLEM OF CAPUTO FRACTIONAL-ORDER DIFFERENTIAL EQUATION

A NUMERICAL ALGORITHM TO INITIAL VALUE PROBLEM OF CAPUTO FRA...

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ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference

作者： Bai, Lu Xue, Dingyu Northeastern Univ Sch Informat Sci & Engn Shenyang 110004 Liaoning Peoples R China Shenyang Univ Sch Informat Engn Shenyang 110044 Liaoning Peoples R China

ISBN: (纸本)9780791857199

A numerical algorithm is presented to solve the initial value problem of linear and nonlinear Caputo fractional-order differential equations. Firstly, nonzero initial value problem should be transformed into zero initial value problem. Error analysis has been done to polynomial algorithm, the reason has been found why the calculation error of the algorithm is large. A new algorithm called exponential function algorithm is proposed based on the analysis. The obtained fractional-order differential equation is transformed into difference equation. If the differential equation is linear, the obtained difference equation is explicit, the numerical solution can be solved directly;otherwise, the obtained difference equation is implicit, the predictor of the numerical solution can be obtained with extrapolation algorithm, substitute the predictor into the equation, the corrector can be solved. Error analysis has been done to the new algorithm, the algorithm is of first order.

关键词： differential equation fractional-order initial value problem numerical algorithm

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A numerical algorithm TO INITIAL VALUE PROBLEM OF LINEAR CAPUTO FRACTIONAL-ORDER DIFFERENTIAL EQUATION

A NUMERICAL ALGORITHM TO INITIAL VALUE PROBLEM OF LINEAR CAP...

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ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference

作者： Bai, Lu Xue, Dingyu Northeastern Univ Sch Informat Sci & Engn Shenyang 110004 Liaoning Peoples R China Shenyang Univ Sch Informat Engn Shenyang 110044 Liaoning Peoples R China

ISBN: (纸本)9780791857199

A numerical algorithm is presented to solve the initial value problem of linear Caputo fractional-order differential equations. Error analysis has been done to Taylor series algorithm, the reason has been found why the error of the algorithm is large, the condition of using Taylor series algorithm is presented. A new algorithm called exponential function algorithm is proposed based on the analysis. Nonzero initial value problem could be transformed into zero initial value problem. The obtained fractional order differential equation is transformed into difference equation, the numerical solution can be found with closed form solution formula. The error of the numerical solution can be modified with prediction-correction algorithm.

关键词： differential equation fractional-order initial value problem numerical algorithm

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Review on numerical algorithms for solving general dynamic equations of the acoustic agglomeration

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RENEWABLE & SUSTAINABLE ENERGY REVIEWS 2025年 217卷

作者： Wang, Xin Liu, Shuang Li, Tian Li, Dekang Univ Shanghai Sci & Technol Shanghai 200093 Peoples R China Ind & Commercial Bank China Ltd Shanghai 330038 Peoples R China

Owing to the rapid growth of advanced manufacturing, particulate pollutants generated during machining processes pose significant risks to human health, equipment safety, atmosphere quality and climate. Current industrial control technologies struggle to effectively remove these particles. Acoustic agglomeration technology is an effective particle pretreatment that uses acoustic waves to facilitate the growth and subsequent removal of particles. Particle dynamics simulation is adept at depicting particle acoustic agglomeration. It utilises numerical algorithms to address the general dynamic equation (GDE), which quantifies the evolution of particle dynamics. Using conventional numerical techniques to solve the GDE is challenging because of its typical partial integrodifferential nature and the intricate agglomeration mechanisms it encompasses. Therefore, drawing on acoustic agglomeration GDE, the research provide a comprehensive review of the characteristics and recent research progress of various algorithms used to solve the GDE of acoustic agglomeration, including method of moments, partition method, the Monte Carlo (MC) algorithm and discrete element method (DEM). MC algorithm, DEM and the coupling of DEM and other method are reviewed in detail. Finally, limitations and future opportunities are discussed about algorithm's applications. This review offers valuable insights into visualising particle acoustic agglomeration, elucidating its microscopic mechanisms and predicting its macroscopic effects on particle agglomeration. Meanwhile, it provides a comprehensive perspective for the optimization, integration and innovation of subsequent numerical algorithms. Thereby, the healthy industrial environment is established, and the achievement of the Sustainable Development Goals is advanced.

关键词： Acoustic agglomeration General dynamic equation Particle size distribution numerical algorithm Monte Carlo algorithm Discrete element method

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Research on Steward Dynamic Platform Simulation numerical algorithm

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International Journal of Plant Engineering and Management 2015年第4期20卷 225-232页

作者： WANG Ming-wei HU De-ji Tianjin University of Technology and Education

In order to achieve attitude control of the six degrees of freedom steward dynamic platform, as well as the real time simulation cockpit attitude, Washout Filtering method was adopted in this paper as the simulation algorithm to derive Washout Fiher high-pass, low-pass filter transfer functions into a differential equation algorithm and longitudinal acceleration tilt strategy, pitching strategies etc. Experimental examples are used to verify correctness of the algorithm.

关键词： simulation algorithm steward dynamic platform numerical algorithm

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numerical analysis of non-proportional biaxial reverse experiments with a two-surface anisotropic cyclic plasticity-damage approach

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2024年 419卷

作者： Wei, Zhichao Gerke, Steffen Bruenig, Michael Univ Bundeswehr Munchen Inst Mech & Statik Werner Heisenberg Weg 39 D-85577 Neubiberg Germany

This paper deals with the numerical analysis of ductile damage and fracture behavior under non -proportional biaxial reverse loading conditions. A two-surface anisotropic cyclic elastic-plastic-damage continuum model is adequately presented, which takes into account the Bauschinger effect, the stress-differential effect, and the change of hardening rate after reverse loading. An efficient Euler explicit numerical integration algorithm, based on the inelastic (plastic or plastic -damage) predictor-elastic corrector approach, is utilized to analyze the stress and finite strain loading histories. Detailed discussions are provided on different numerical integration-related consistent tangent operators that achieve convergence within the global Newton-Raphson scheme. The proposed continuum model is implemented into the commercial software Ansys as a user-defined subroutine (UMAT). Furthermore, the novel non-proportional biaxial tensile reverse experiments are performed to validate the proposed continuum model. The associated numerical simulations investigate the stability and accuracy of the proposed algorithm and material model.

关键词： Ductile damage and fracture Reverse loading Non-proportional biaxial experiments numerical algorithm Finite strains

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numerical Solution of Second-Order Impulsive Differential Equations With Loadings Subject to Integral Boundary Conditions

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2025年第6期48卷 6269-6277页

作者： Kadirbayeva, Zhazira Kadirbayeva, Roza Inst Math & Math Modeling Alma Ata Kazakhstan Kazakh Natl Womens Teacher Training Univ Alma Ata Kazakhstan Int Informat Technol Univ Alma Ata Kazakhstan South Kazakhstan Pedag Univ Shymkent Kazakhstan

In this paper, we present a computational method for solving the second-order impulsive differential equations with loadings subject to integral boundary conditions based on the Dzhumabaev parametrization method. The idea of this method involves introducing additional parameters, reducing the original problem to solving a system of linear algebraic equations. The system's coefficients and right-hand side are determined by solving Cauchy problems for ODEs and by calculating definite integrals. Four examples are provided to show the effectiveness and feasibility of the main results.

关键词： impulsive differential equations integral conditions loadings numerical algorithm parametrization method

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Research of Steward Dynamic Platform Simulation numerical algorithm

科学导报

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科学导报 2015年第20期 214-216页

作者： Wang Mingwei Hu Deji Tianjin China Tianjin University of Technology and Education300222

In order to achieve attitude control of the six degrees of freedom Steward dynamic platform, as well as the real time simulation cockpit attitude, Washout Filtering method was adopted in this paper as the simulation algorithm to derive Washout Filter high-pass, low-pass filter transfer function into a differential equation algorithm and longitudinal acceleration tilt strategy, pitching strategies etc. Experimental examples are used to verify correctness of the algorithm.

关键词： simulation algorithm Steward dynamic platform numerical algorithm

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Entropy optimization and Prandtl-Eyring non-Newtonian fluid flow with second-order slip conditions past a curved Riga sheet;numerical simulation

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INTERNATIONAL JOURNAL OF THERMAL SCIENCES 2025年 214卷

作者： Ali, Bilal Zhou, Yue-Ting Jubair, Sidra Tariq, Muzammal Hameed Kumar, Abhinav Siddiqui, Md Irfanul Haque Tongji Univ Sch Aerosp Engn & Appl Mech Shanghai 200092 Peoples R China Shanghai Inst Aircraft Mech & Control 100 Zhangwu Rd Shanghai 200092 Peoples R China Dalian Univ Technol Sch Math Sci Dalian 116024 Peoples R China Ural Fed Univ Dept Nucl & Renewable Energy Ekaterinburg 620002 Russia Karpagam Acad Higher Educ Dept Mech Engn Coimbatore 641021 India Western Caspian Univ Dept Tech Sci Baku Azerbaijan King Saud Univ Coll Engn Dept Mech Engn Riyadh 12372 Saudi Arabia

The non-Newtonian (NN) Prandtl-Eyring fluid (PEF) model can be used to optimize conditions for processing, ensure substance high quality and consistency, and anticipate melted polymer flow behavior. This paper looks into an intriguing feature of irreversibility estimation through NN-PEF flow over a curved Riga surface. The impact of second-order slip conditions, thermal radiation, and exponential heat source/sink are also elaborated. The flow equations of NN-PEF have been reformulated into a dimensionless representation of differential equations (DEs) with an application of similarity conversions. The obtained lowest-order differential equations are numerically solved through the PCM (parametric continuation method). For accuracy of the results, the outcomes are compared to both experimental and theoretical results. The relative percent error between the present findings and the published numerical results at Re = 5000 is 0.71094 %. The rate of heat transfer (W/ m2K) enhances from 4238.0724 to 44390.4205 at Re = 1594 to 440. The relative error between published experimental and present results is about 0.0029 % at Re = 440, which ensures the reliability of the proposed model and applied methodology. The velocity field of PEF is significantly boosted with the positive variation in 1st and 2nd order slip parameters. The influence of the Brinkmann number and heat radiation factor is enhanced, while the consequences of the temperature ratio parameter drop the rate of entropy generation in the system.

关键词： Entropy optimization Experimental validation Second-order slip conditions Non-Newtonian Prandtl-Eyring fluid numerical algorithm Curved Riga sheet

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