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numerical algorithm for constructing Lyapunov functions of polynomial differential system

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2009年第1-2期29卷 247-262页

作者： Lin, Xiao-Lin Jiang, Yao-Lin Xi An Jiao Tong Univ Dept Math Sci Xian 710049 Peoples R China

In this paper, a numerical algorithm for constructing Laypunov functions of polynomial system is described. The algorithm is described for second-dimension system although extension to higher dimension systems would appear to be possible. Using the algorithm, we can obtain the estimation of asymptotic stability regions of nonlinear autonomous dynamical systems. numerical examples further illustrate the theoretical work in this paper.

关键词： numerical algorithm Lyapunov function Asymptotic stability region Polynomial differential system

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A Newton-like algorithm for L₂-gain optimal control of an electro-hydraulic servo-system 22

A Newton-like algorithm for <i>L</i><sub>2</sub>-gain optima...

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22nd Mediterranean Conference on Control and Automation (MED)

作者： Milic, Vladimir Kasac, Josip Situm, Zeljko Univ Zagreb Fac Mech Engn & Naval Architecture HR-10000 Zagreb Croatia

ISBN: (纸本)9781479959013

This paper is concerned with L-2-gain optimal control approach for rotary electro-hydraulic servo-system. The electro-hydraulic dynamics with respect to hydraulic motor velocity, with input voltage to the servo valve as control input and load torque as disturbance input, is formulated. The mathematical model results in input-affine nonlinear system. A numerical algorithm based on Newton method to solve a finite-horizon minimax problem for L-2-gain minimisation of electro-hydraulic system is presented. The feedback control and disturbance variables are formulated as linear combination of approximation functions. The proposed algorithm, which has recursive matrix structure, directly finds approximations of the feedback control and the "worst case" disturbance variables. Developed controller has been tested experimentally in the laboratory model of an electro-hydraulic servo system.

关键词： Newton method electrohydraulic control equipment feedback matrix algebra minimax techniques nonlinear systems optimal control servomechanisms torque torque control Newton-like algorithm approximation functions electrohydraulic dynamics feedback control finite horizon minimax problem hydraulic motor velocity input-affine nonlinear system laboratory model load torque mathematical model numerical algorithm recursive matrix structure rotary electrohydraulic servo system servo valve worst case disturbance variables Approximation methods Heuristic algorithms Induction motors Mathematical model Servomotors Torque Valves

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A numerical Analysis of the M/G/1/N Queue with Vacations

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IFAC Proceedings Volumes 2014年第2期47卷 504-509页

作者： Sofiane Ouazine Karim Abbas Department of Mathematics Exact Sciences Faculty University of Bejaia Campus of Targua Ouzemour 06000 Bejaia Algeria LAMOS Laboratory Exact Sciences Faculty University of Bejaia Campus of Targua Ouzemour 06000 Bejaia Algeria

In this paper we discuss the applicability of a computational approach based on a Taylor series expansion for the numerical evaluation of the M/G/1/N queueing model with, so called, working vacations and vacation interruptions. Specifically, we develop the performance measures of the considered system into a Taylor series with respect to the vacation parameter. Our objective is to understand how the vacation rate affects the system performance. numerical results are carried out to illustrate the efficiency of our approach.

关键词： Taylor series expansion numerical algorithm Queues Vacations Performance measures Deviation matrix

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An efficient numerical algorithm for stability testing of fractional-delay systems

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ISA TRANSACTIONS 2009年第1期48卷 32-37页

作者： Merrikh-Bayat, Farshad Karimi-Ghartemani, Masoud Sharif Univ Technol Tehran Iran

This paper presents a numerical algorithm for BIBO stability testing of a certain class of the so-called fractional-delay systems. The characteristic function of the systems under consideration is a multi-valued function of the Laplace variable s which is defined on a Riemann surface with finite number of Riemann sheets where the origin is a branch point. The stability analysis of such systems is not straightforward because there is no universally applicable analytical method to find the roots of the characteristic equation on the right half-plane of the first Riemann sheet. The proposed method is based on the Rouche's theorem which provides the number of the zeros of a given function in a given simple closed contour. One advantage of the proposed method over previous works is that it gives the number and the location of the unstable poles. The algorithm has a reliable result which is illustrated by several examples. (C) 2008 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： Fractional delay equation Stability analysis numerical algorithm Fractional-order system

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Decomposition based least squares iterative estimation algorithm for output error moving average systems

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ENGINEERING COMPUTATIONS 2014年第4期31卷 709-725页

作者： Zhang, Wenge Jiangnan Univ Minist Educ Key Lab Adv Proc Control Light Ind Wuxi Peoples R China

Purpose - The purpose of this paper is to solve the heavy computational problem of parameter estimation algorithm. Design/methodology/approach - Presents a decomposition least squares based iterative identification algorithm. Findings - Can estimate the parameters for linear or pseudo-linear systems and have lower computational burden. Originality/value - This paper adopts a decomposition technique to solve engineering computation problems and offers a potential and efficient algorithm.

关键词： Computation method numerical algorithm

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Real-time Trajectory Planning for Rail Transit Train Considering Regenerative Energy

Real-time Trajectory Planning for Rail Transit Train Conside...

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IEEE International Conference on Intelligent Transportation Systems

作者： Jianwei Qu Xiaoyun Feng Qingyuan Wang Sch. of Electr. Eng. Southwest Jiaotong Univ. Chengdu China

ISBN: (纸本)9781479960798

This paper proposes an energy efficient driving strategy considering regenerative braking energy, arbitrary speed limits, variable grade profiles and curve radius. In actual operation, the reference speed curve of the Automatic Train Operation (ATO) system needs on-line recalculation when the operation circumstances change, such as delay or a temporary speed limit. An energy-efficient operation optimization model with arbitrary feasible initial and final velocities is built, and the optimal operation modes are obtained by means of the maximum principle. When the braking energy is fully recovered, the speed-holding operation mode is proved to be the most energy-saving regime. Then a numerical algorithm is presented to construct the energy saving speed curve for a given time with the consideration of speed limits. The feasibility of the algorithm is verified through the case study of Shenzhen Metro Line 1. With the flexibility of arbitrary initial and final speed values, the presented algorithm can be applied to ATO system for real-time calculation.

关键词： energy conservation numerical analysis optimisation path planning rapid transit systems regenerative braking ATO system Shenzhen Metro Line 1 arbitrary speed limits automatic train operation braking energy curve radius energy efficient driving strategy energy-efficient operation optimization model energy-saving regime numerical algorithm on-line recalculation optimal operation modes rail transit train real-time trajectory planning regenerative braking energy regenerative energy speed-holding operation mode variable grade profiles Energy efficiency Force Optimization Rail transportation Rails Trajectory

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numerical Computing With Modern Fortran

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丛书名： Other Titles in Applied Mathematics

2013年

作者： Richard J. Hanson Tim Hopkins

ISBN: (数字)9781611973129

ISBN: (纸本)9781611973112

The Fortran language standard has undergone significant upgrades in recent years (1990, 1995, 2003, and 2008). numerical Computing with Modern Fortran illustrates many of these improvements through practical solutions to a number of scientific and engineering problems. Readers will discover techniques for modernizing algorithms written in Fortran; examples of Fortran interoperating with C or C++ programs, plus using the IEEE floating-point standard for efficiency; illustrations of parallel Fortran programming using coarrays, MPI, and OpenMP; and a supplementary website with downloadable source codes discussed in the book. Audience: This book is intended for Fortran programmers seeking to update their programming skills using the language s latest features and for C and C++ programmers who want to understand key software aspects of numerical computing using modern Fortran. It is suitable for an upper-level undergraduate or early graduate course on advanced numerical scientific computing. Contents: Introduction; Chapter 1: The Modern Fortran Source; Chapter 2: Modules for Subprogram Libraries; Chapter 3: Generic Subprograms; Chapter 4: Sparse Matrices, Defined Operations, Overloaded Assignment; Chapter 5: Object-Oriented Programming for numerical Applications; Chapter 6: Recursion in Fortran; Chapter 7: Case Study: Toward a Modern QUADPACK Routine; Chapter 8: Case Study: Quadrature Routine qag2003; Chapter 9: IEEE Arithmetic Features and Exception Handling; Chapter 10: Interoperability with C; Chapter 11: Defined Operations for Sparse Matrix Solutions; Chapter 12: Case Study: Two Sparse Least-Squares System Examples; Chapter 13: Message Passing with MPI in Standard Fortran; Chapter 14: Coarrays in Standard Fortran; Chapter 15: OpenMP in Fortran; Chapter 16: Modifying Source to Remove Obsolescent or Deleted Features; Chapter 17: Software Testing; Chapter 18: Compilers; Chapter 19: Software Tools; Chapter 20: Fortran Book Code on SIAM Web Site; Bibliography; Index.

关键词： numerical application Fortran source code numerical algorithm scientific programming

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High-order adaptive method for computing two-dimensional invariant manifolds of three-dimensional maps

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COMMUNICATIONS IN NONLINEAR SCIENCE AND numerical SIMULATION 2013年第7期18卷 1734-1745页

作者： Wrobel, Jacek K. Goodman, Roy H. New Jersey Inst Technol Dept Math Sci Newark NJ 07102 USA

An efficient and accurate numerical method is presented for computing invariant manifolds of maps which arise in the study of dynamical systems. A quasi-interpolation method due to Hering-Bertram et al. is used to decrease the number of points needed to compute a portion of the manifold. Bezier triangular patches are used in this construction, together with adaptivity conditions based on properties of these patches. Several numerical tests are performed, which show the method to compare favorably with previous approaches. (C) 2012 Elsevier B. V. All rights reserved.

关键词： Invariant manifold Computer-aided geometric design numerical algorithm

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Strong solutions of a class of hybrid diffusion processes with state-dependent regime-switching

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APPLIED numerical MATHEMATICS 2013年 72卷 72-90页

作者： Rathinasamy, A. Yin, Baojian PSG Coll Technol Dept Math Coimbatore 641004 Tamil Nadu India Huazhong Univ Sci & Technol Sch Math & Stat Wuhan 430074 Hubei Peoples R China

This work focuses on the strong solutions of a class of hybrid diffusion processes with state-dependent regime-switching. This important class of processes originates from the purpose of modeling the interest rate in finance. They have no any explicit solutions. Moreover, state-dependent regime-switching and non-Lipschitz diffusion coefficient pose a challenge to our analysis. To overcome all of these, we consider the Euler numerical schemes rather than the traditional Picard iterations in the existing results of solutions of stochastic differential equations. The weak convergence of numerical algorithms is first established by a martingale problem formulation. Using this result, we can also obtain the strong convergence of the algorithms. The existence of strong solutions is then confirmed. In addition, decreasing stepsize iterative algorithms and their weak convergence are presented. Several numerical experiments are also provided for illustration. (C) 2013 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Hybrid diffusion numerical algorithm Convergence Strong solution

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Microplane model M7f for fiber reinforced concrete

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ENGINEERING FRACTURE MECHANICS 2013年 105卷 41-57页

作者： Caner, Ferhun C. Bazant, Zdenek P. Wendner, Roman Tech Univ Catalonia Inst Energy Technol Barcelona 08028 Spain Northwestern Univ Dept Civil & Environm Engn Evanston IL 60208 USA

Model M7f is a new model for fiber reinforced concretes under static and dynamic loads, which features two kinds of improvement over the earlier versions: (I) It is built on M7, a new, greatly improved, microplane model for plain concrete;and (2) it includes a more realistic description of the fiber pullout and breakage. The former include: (a) the absence of volumetric deviatoric split of elastic strains, which eliminates excessive lateral expansions or contractions and stress locking in far post-peak extensions;(b) simulation of the differences between hydrostatic compression and uniaxial compression under rigid lateral confinement;and (c) high shear dilatancy of low strength concretes;and realistic description of unloading, reloading and load cycles, even if they cross between tension and compression. The latter includes an improved continuous dependence of the effect of fibers on the fiber volume fraction. The fiber resistance is a function of the strain representing the average opening of cracks of given spacing and, as in model M5f, a horizontal plateau as a function of the type of fiber and fiber volume fraction has been employed and used systematically for all fits. In this study, this horizontal plateau is justified using uniformly distributed crack bridging fibers. The model behavior is calibrated and verified by fitting of the main test data from the literature. The match of experimental observations and the computational results is closer than in the previous models. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Constitutive modeling Fiber reinforced concrete Inelastic behavior Cracking damage Fracture Softening numerical algorithm Thermodynamic potentials Unloading Cyclic loading

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