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Libration control of tethered satellites in elliptical orbits

JOURNAL OF SPACECRAFT AND ROCKETS 2006年第2期43卷 476-479页

作者： Williams, P RMIT Univ Sch Aerosp Mech & Mfg Engn Melbourne Vic 3083 Australia

A strategy for the control of the librations of a tethered satellite systemin elliptic orbits using tether length control, which drives the system to controlled periodiclibration trajectories, is suggested. There is a range of eccentricities up to about 0.4453 forwhich no length variations are needed for the system to follow the periodic trajectory. Above thiseccentricity, it is necessary to vary the length of tether to maintain a periodic trajectory. Themethod for finding these trajectories to minimize the control input utilizes a collocation ***-loop stability is provided by a linear feedback control law, whose feedback gains are alsoperiodic. Consequently, Floquet theory demonstrates the stability of the closed-loop system.

关键词： Satellites Elliptical Orbit Closed Loop Control Feedback Control Tethered Satellite System Nonlinear programming sequential quadratic programming Atmospheric Drag Propellant FORTRAN

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Design of skid landing gears by means of multibody optimization

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JOURNAL OF AIRCRAFT 2006年第2期43卷 555-563页

作者： Airoldi, A Lanzi, L Politecn Milan Dipartimento Ingn Aerospaziale I-20156 Milan Italy

This paper discusses a numerical approach to the design of skid landing gears, based on an optimization procedure linked to a multibody explicit c ode. The modeling technique has been validated with the experimental results of a drop test considering the overall landing performances as well as the levels of bending strains developed along the cross members. According to the presented numerical-experimental correlations, the numerical analyses obtained appreciable results at a very low computational cost. The technique has been applied to generate a parameterized model of a skid landing-gear, suitable to be adopted in an automatic optimization procedure. To adequately formulate the optimization process, the basic aspects involved in the design of skid landing gears have been reviewed, and two optimization procedures have been developed. These formulations have been directed, respectively, to optimize the landing performances and to obtain an optimal plastic strain distribution along the cross members axes. The optimization search applied to different design tasks shows that the developed numerical tools can identify well-sized landing-gear configurations that satisfy all of the imposed constraints on the landing performances and are characterized by uniform strain distributions along the cross members, thus maximizing the strength and the durability of the landing system.

关键词： Landing Gear Helicopters Strain Distribution Landing Performance Finite Element Modeling Structural Element sequential quadratic programming Civil Aviation Regulation Friction Coefficient Ultimate Strength

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Supercalm multifunctions for convergence analysis

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SET-VALUED ANALYSIS 2006年第3期14卷 249-261页

作者： Levy, Adam B. Bowdoin Coll Dept Math Brunswick ME 04011 USA

Calmness of multifunctions is a well-studied concept of generalized continuity in which single-valued selections from the image sets of the multifunction exhibit a restricted type of local Lipschitz continuity where the base point is fixed as one point of comparison. Generalized continuity properties of multifunctions like calmness can be applied to convergence analysis when the multifunction appropriately represents the iterates generated by some algorithm. Since it involves an essentially linear relationship between input and output, calmness gives essentially linear convergence results when it is applied directly to convergence analysis. We introduce a new continuity concept called 'supercalmness' where arbitrarily small calmness constants can be obtained near the base point, which leads to essentially superlinear convergence results. We also explore partial supercalmness and use a well-known generalized derivative to characterize both when a multifunction is supercalm and when it is partially supercalm. To illustrate the value of such characterizations, we explore in detail a new example of a general primal sequential quadratic programming method for nonlinear programming and obtain verifiable conditions to ensure convergence at a superlinear rate.

关键词： calmness multifunctions generalized continuity variational analysis convergence analysis sequential quadratic programming

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Using eigenstructure of the Hessian to reduce the dimension of the intensity modulated radiation therapy optimization problem

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ANNALS OF OPERATIONS RESEARCH 2006年第1期148卷 81-94页

作者： Carlsson, Fredrik Forsgren, Anders Rehbinder, Henrik Eriksson, Kjell Royal Inst Technol KTH Dept Math SE-10044 Stockholm Sweden RaySearch Labs SE-11134 Stockholm Sweden

Optimization is of vital importance when performing intensity modulated radiation therapy to treat cancer tumors. The optimization problem is typically large-scale with a nonlinear objective function and bounds on the variables, and we solve it using a quasi-Newton sequential quadratic programming method. This study investigates the effect on the optimal solution, and hence treatment outcome, when solving an approximate optimization problem of lower dimension. Through a spectral decompostion, eigenvectors and eigenvalues of an approximation to the Hessian are computed. An approximate optimization problem of reduced dimension is formulated by introducing eigenvector weights as optimization parameters, where only eigenvectors corresponding to large eigenvalues are included. The approach is evaluated on a clinical prostate case. Compared to bixel weight optimization, eigenvector weight optimization with few parameters results in faster initial decline in the objective function, but with inferior final solution. Another approach, which combines eigenvector weights and bixel weights as variables, gives lower final objective values than what bixel weight optimization does. However, this advantage comes at the expense of the pre-computational time for the spectral decomposition.

关键词： IMRT optimization sequential quadratic programming quasi-Newton method

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Newton-type methods for constrained optimization with nonregular constraints

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Computational Mathematics and Mathematical Physics 2006年第8期46卷 1299-1319页

作者： Golishnikov, M.M. Izmailov, A.F. Faculty of Computational Mathematics and Cybernetics Moscow State University Leninskie gory Moscow 119992 Russian Federation

The most important classes of Newton-type methods for solving constrained optimization problems are discussed. These are the sequential quadratic programming methods, active set methods, and semismooth Newton methods for Karush-Kuhn-Tucker systems. The emphasis is placed on the behavior of these methods and their special modifications in the case where assumptions concerning constraint qualifications are relaxed or altogether dropped. Applications to optimization problems with complementarity constraints are examined. © MAIK "Nauka/Interperiodica".

关键词： Active set methods Constrained optimization problems Constraint qualifications Newton-type methods Semismooth Newton methods sequential quadratic programming

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Reactive power optimization algorithm. based on trust-region global SQP

Reactive power optimization algorithm. based on trust-region...

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General Meeting of the Power-Engineering-Society

作者： Zhou, Renjun Zhang, Yanping Liu, Jianhua Changsha Univ Sci & Technol Coll Elect Engn Changsha 410076 Peoples R China

ISBN: (纸本)9781424404926

In order to improve the convergence and calculate optimal results reliably and accurately, a trust-region algorithm based on global sequential quadratic programming (SQP) Is presented for reactive power optimization. This method combines global SQP with trust-region method. The method of decomposed inaccurate direction component is adopted to compute trust-region sub problem to guarantee feasible region of this sub problem is not null. The penalty parameter is effectively regulated in Merit Function to avoid the Marotos Effect. This example of the computation shows that this algorithm has global convergence and is fast, accurate and reliable.

关键词： reactive power optimization trust-region method sequential quadratic programming global convergence

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Combining flux and energy balance analysis to model large-scale biochemical networks

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Journal of Bioinformatics and Computational Biology 2006年第6期4卷 1227-1243页

作者： Heuett, William J. Qian, Hong Department of Physics University of Colorado Boulder CO 80309-0390 United States Department of Applied Mathematics University of Washington Seattle WA 98195-2420 Box 352420 United States

Stoichiometric Network Theory is a constraints-based, optimization approach for quantitative analysis of the phenotypes of large-scale biochemical networks that avoids the use of detailed kinetics. This approach uses the reaction stoichiometric matrix in conjunction with constraints provided by flux balance and energy balance to guarantee mass conserved and thermodynamically allowable predictions. However, the flux and energy balance constraints have not been effectively applied simultaneously on the genome scale because optimization under the combined constraints is non-linear. In this paper, a sequential quadratic programming algorithm that solves the non-linear optimization problem is introduced. A simple example and the system of fermentation in Saccharomyces cerevisiae are used to illustrate the new method. The algorithm allows the use of non-linear objective functions. As a result, we suggest a novel optimization with respect to the heat dissipation rate of a system. We also emphasize the importance of incorporating interactions between a model network and its surroundings. © Imperial College Press.

关键词： Constraints-based optimization Reaction networks sequential quadratic programming Stoichiometric Network Theory Systems biology Yeast glycolysis

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Low-thrust transfer orbit design based on Lyapunov feedback control law

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IMACS Multiconference on Computational Engineering in Systems Applications (CESA 2006)

作者： Ren Yuan Cui Pingyuan Luan Enjie Harbin Inst Technol Deep Space Explorat Res Ctr POB 3030Sci Pl Harbin 150006 Peoples R China China Natl Space Adm Beijing Peoples R China

ISBN: (纸本)9787302139225

A novel low-thrust orbit transfer design method is presented which is based on the knowledge of optimal thrust direction and optimal location for changing each of the orbit elements and the concept of Lyapunov feed back control. In this method, a set of equinoctial elements is utilized to avoid the singularities in dynamical equation of classical orbit elements. A thruster switch law is derived by analyzing the effectivity of the changing of each orbit elements. The thrust will be cut-off if the effectivity is below a specified level. When on, the thrust is a constant. The two-body dynamics model is used in this method. The method needs few input parameters. By sequential quadratic programming (SQP), these parameters could be adjusted and performance index could be maximized. This method is a simple way to estimate key parameters of a low-thrust orbit transfer and could also give an accurate initial guesses for the future optimization.

关键词： Lyapunov feed back control low-thrust sequential quadratic programming

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Airfoil shape optimization using a nonuniform rational B-splines parameterization under thickness constraint

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AIAA JOURNAL 2006年第10期44卷 2170-2178页

作者： Painchaud-Ouellet, Simon Tribes, Christophe Trepanier, Jean-Yves Pelletier, Dominique Ecole Polytech Montreal PQ H3C 3A7 Canada

Results for 2-D airfoil shape optimization in transonic regime are presented. Airfoil shapes are represented by nonuniform rational B-splines with appropriate regularity properties. A Navier-Stokes How solver is used to compute the flow field and to obtain aerodynamic coefficients. A design of experiment is conducted to select the most sensitive design variables among the nonuniform rational B-splines parameters to reduce their number in the final optimization process. Single-point and multipoint formulations of the optimization problem are proposed and compared. The nonuniform rational B-splines parameterization guarantees smooth optimized airfoils. The multipoint optimization formulation combined with the nonuniform rational B-splines parameterization leads to airfoils with good performance over a specified Mach range.

关键词： Shape Optimization B Splines Supercritical Airfoils Aerodynamic Coefficients Design of Experiments Aerodynamic Performance sequential quadratic programming CFD Reynolds Averaged Navier Stokes Friction Coefficient

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The use of an SQP algorithm in slope stability analysis

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COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING 2005年第1期21卷 23-37页

作者： Chen, J Yin, JH Lee, CF Hong Kong Polytech Univ Dept Civil & Struct Engn Kowloon Hong Kong Peoples R China Univ Hong Kong Dept Civil Engn Hong Kong Hong Kong Peoples R China

In the upper bound approach to limit analysis of slope stability based on the rigid finite element method, the search for the minimum factor of safety can be formulated as a non-linear programming problem with equality constraints only based on a yield criterion, a flow rule, boundary conditions, and an energy-work balance equation. Because of the non-linear property of the resulting optimization problems, a non-linear mathematical programming algorithm has to be employed. In this paper, the relations between the numbers of nodes, elements, interfaces, and subsequent unknowns and constraints in the approach have been derived. It can be shown that in the large-scale problems, the unknowns are subject to a highly sparse set of equality constraints. Because of the existence of non-linear equalities in the approach, this paper applies first time a special sequential quadratic programming (SQP) algorithm, feasible SQP (FSQP), to obtain solutions for such non-linear optimization problems. In FSQP algorithm, the non-linear equality constraints are turned into inequality constraints and the objective function is replaced by an exact penalty function which penalizes non-linear equality constraint violations only. Three numerical examples are presented to illustrate the potentialities and efficiencies of the FSQP algorithm in the slope stability analysis. Copyright (C) 2004 John Wiley Sons, Ltd.

关键词： sequential quadratic programming slope stability limit analysis upper bound rigid finite element method non-linear programming

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