PDF下载 分享
[1]胡松启,陈 雨.伪谱法在飞行器轨迹优化中应用分析[J].火箭推进,2014,40(05):61-68.
　HU Song-qi,CHEN Yu.Analysis of pseudospectral methods applied to aircraft trajectory optimization[J].Journal of Rocket Propulsion,2014,40(05):61-68.
点击复制

伪谱法在飞行器轨迹优化中应用分析

《火箭推进》[ISSN:1672-9374/CN:CN 61-1436/V] 卷: 40 期数: 2014年05期 页码: 61-68 栏目: 研究与设计 出版日期: 2014-10-28
Title:
Analysis of pseudospectral methods applied to aircraft trajectory optimization
作者:
胡松启; 陈 雨
西北工业大学 燃烧、热结构与内流场重点实验室，陕西 西安 710072
Author(s):
HU Song-qi;  CHEN Yu
Key Laboratory of Combustion, Thermal Structure and Internal Flow Field, Northwestern Polytechnical University, Xi'an 710072, China
关键词:
伪谱法; 飞行器;  轨迹优化
Keywords:
pseudospectral method;  air vehicle;  trajectory optimization
分类号:
V412-34
文献标志码:
A
摘要:
伪谱法作为一种在飞行器轨迹优化领域广泛应用的方法，国内外缺乏对其进行综合研究分析的相关文献。介绍了伪谱法在飞行器轨迹优化领域的发展现状，详细分析了已应用于飞行器轨迹优化的4种伪谱法的特点和应用情况，总结了这4种方法优缺点：Legendre伪谱法研究较早、应用最为广泛，Gauss伪谱法和Radau伪谱法精度较高，而Chebyshev伪谱法理论上精度高但研究刚起步。伪谱法具有全局特性，计算精度高，收敛快，但也存在缺乏收敛解判定准则、难以处理非光滑问题等不足。介绍了伪谱法在处理bang-bang控制问题时所遇到的困难，对伪谱法的改进工作做出总结：改进算法，研究与其他算法相结合的优化方法。总体而言，伪谱法在轨迹优化问题上的应用前景很广。
Abstract:
The pseudospectral methods are widely used in the field of aircraft trajectory optimization. There is lack of relevant literatures about comprehensive research and analysis on the pseudospectral methods at home and abroad. The development status of the pseudospectral methods in the field of aircraft trajectory optimization is described in this paper. The characteristics, application situation, advantages and disadvantages of the four common pseudospectral methods are analyzed. They are Legendre pseudospectral method, Gauss pseudospectral method, Radau pseudo-spectral method and Chebyshev pseudospectral method. Difficulty in dealing with bang-bang control problems is introduced . The improvement about the pseudospectral methods are summarized. The algorithm was improved and some optimization methods combining with other algorithms were studied. Generally speaking, the pseudospectral methods have a wide application prospect in the trajectory optimization.

参考文献/References:

[1]BETTS J T. Survey numerical methods for trajectory optimization[J]. AIAA Journal of Guidance Control and Dynamics, 1998, 21(2): 193-207.
[2]BETTS J T. Practical methods for optimal control using nonlinear programming[M]. Philadelphia: Society for Industrial and Applied Mathematics, 2001.
[3]VLASSENBROECK J, DOOREN R V. A Chebyshev technique for solving nonlinear optimal problems[J]. IEEE Transactions on Automatic Control, 1988, 33(4): 333-340.
[4]ELNAGAR J, KAZEMI M A, RAZZAGHI M. The pseudospectral Legendre method for discretizing optimal control problems[J]. IEEE Transactions on Automatic Control, 1995, 40(10): 1793-1796.
[5]雍恩米, 陈磊, 唐国金. 飞行器轨迹优化数值方法综述[J]. 宇航学报, 2008, 29(2): 398-406.
[6]TREFETHEN L N. Spectral methods in MATLAB[M]. Philadelphia: Society for Industrial and Applied Mathematics, 2000.
[7]FAHROO F, ROSS M I. Costate estimation by a Legendre pesudospectral method[J]. AIAA Journal of Guidance Control and Dynamics, 2001, 24(2): 270-277.
[8]ROSS M I, FAHROO F. Convergence of pseudospectral discretizations of optimal control problems[C]// IEEE Conference on Decision and Control.[S.l.]: IEEE, 2001: 3175-3177.
[9]RAO A V, CLARKE K A. Perfomance optimization of a maneuvering reentry vehicle usinga Legendre pseudospectral method[C]// AIAA Atmospheric Flight Mechanics Conference. Monterey: AIAA, 2002: 111-121.
[10]STANTON S, PROULX R. Optimal orbital transfer using a Legendre pseudospectral method[C]// AAS/AIAA Astrodynamics Specialist Conference. Montana: AIAA, 2003: 222-232.
[11]KARPENKO M, BHATT S, BEDROSSIAN N, el at. Flight implementation of pseudospectral optimal control for the TRACE space telescope[C]// AIAA Guidance Navigation and Control Conference. Oregon, Portland: AIAA, 2011: 11-18.
[12]张侃. 基于多任务多目标的空天飞行器轨迹设计及优化研究[D]. 南京: 南京航空航天大学, 2010.
[13]梅杰, 马广富, 杨博. 基于Legendre伪谱法的卫星轨道转移燃料最优控制[J]. 哈尔滨工业大学学报, 2010, 42(3): 352-357.
[14]BENSON D. A gauss pseudospectral transcription for optimal control[D]. Massachusetts, USA: Massachusetts Institute of Technology, 2004.
[15]BENSON A, THORVALDSEN T, RAO V. Direct trajectory optimization and costate estimation via an orthogonal collocation method [J]. IEEE Journal of Guidance Control and Dynamics, 2006, 29(6): 1435-1440.
[16]HUNTINGTON G T, RAO A V. Optimal reconfiguration of spacecraft formation using the Gauss pseudospectral method[J]. AIAA Journal of Guidance Control and Dynamics, 2008, 31(3): 689-698.
[17]HUNTINGTON G T, GEOFFREY T, BESON D A, et al. Computation of boundary controls using a gauss pseudospectral method[J]. Advances in the Astronautical Sciences, 2007, 129(3): 2049-2067.
[18]GARG D, WILLIAM W H, RAO A V. Gauss pseudospectral method for solving infinite-horizon optimal control problems[C]// AIAA Guidance Navigation Control Conference. Toronto, Ontario, Canada: AIAA, 2010: 1011-1020.
[19]雍恩米, 唐国金, 陈磊. 基于Gauss伪谱方法的高超声速飞行器再入轨迹快速优化[J]. 宇航学报, 2008, 29(6): 1766-1772.
[20]姚寅伟, 李华滨. 基于Gauss伪谱法的高超声速飞行器多约束三维再入轨迹优化[J].航天控制, 2012, 30(2):33-38.
[21]FAHROO F, ROSS I. Pseudospectral methods for infinite horizon nonlinear optimal control problem[C]// AIAA Guidance Navigation and Control Conference. San Francisco: AIAA, 2005: 595-599.
[22]KAMESWARAN S, BIEGLER L T. Convergence rates for direct transcription of optimal control problems at Radau points[C]// Proceedings of the 2006 American Control Conference. Minneapolis, Minnesota: [s.n.], 2006: 121-128.
[23]GARG D, PATTERSON M A, DARBY C L, et al. Direct trajectory optimization and costate estimation of general optimal control problems using a Radau pseudospectral method[C]// AIAA Guidance Navigation and Control Conference. Chicago, Illinois: AIAA, 2009: 40-50.
[24]GARG D, MICHAEL A. Direct trajectory optimization and costate estimation of finite-horizon and infinite-horizon optimal control problems using a Radau pseudospectral method[J]. Computational Optimization and Applications, 2011, 49(2): 335-358.
[25]王铀, 赵辉, 惠百斌, 等. 利用Radau伪谱法求解UCAV对地攻击轨迹研究[J]. 电光与控制, 2012, 19(10): 50-53.
[26]HUNTINGTON G T. Advancement and analysis of a Gauss pseudospectral transcription for optimal control pmblems[D]. Massachusetts, USA: Massachusetts lnstitiute of Technology, 2007.
[27]GONG Q, ROSS I M, FAHROO F. Costate computation by a Chebyshev pseudospectral method[J]. AIAA Journal of Guidance Conteol and Dynamics, 2010, 33(2): 623-628.
[28]FAHROO F, ROSS I M. Direct trajectory optimization by a Chebyshev pseudospectral method[J]. AIAA Journal of Guidance Control and Dynamics, 2002, 25(1): 160-166.
[29]MIHAILA B, MIHAILA I. Numerical approximation using Chebyshev polynomail expansions[J]. Journal of Physics A-mathematical and General, 2002, 35(9): 731-746.
[30]ELNAGAR G N, KAZEMI M A. Pseudospectral Chebyshev optimal control of constrained nonlinear dynamical systems[J]. Computational Optimization and Applications, 1998, 11(2): 195-217.
[31]万翻良. 航天动力学问题的伪谱迭代求解研究[D]. 长沙: 国防科技大学, 2011.
[32]Hesthaven J, Gottieb S, Gottlieb D. Spectral methods for time-dependent problems[M]. Cambridge: Cambridge University Press, 2007.
[33]郭铁丁. 深空探测小推力轨迹优化的间接法与伪谱法研究[D]. 北京: 清华大学, 2012.
[34]RAO A V. Extension of a pseudospectral Legendre me- thod to nonsequential multiple-phase optimal control problems[C]// AIAA Guidance Navigation and Control Conference and Exhibit. Austin,Texas: AIAA, 2003: 141-149.
[35]ROSS I M, FAHROO F. Pseudospectral knotting me- thods for solving optimal control problem[J]. Journal of Guidance Control and Dynamics, 2004, 27(3): 397-405.
[36]宣颖, 张为华, 张育林. 基于Legendre伪谱法的固体运载火箭轨迹优化研究[J]. 固体技术, 2008, 31(5): 425- 429.
[37]杨希祥, 张为华. 基于Gauss伪谱法的固体运载火箭上升段轨迹快速优化研究[J]. 宇航学报, 2011, 32(1):15-21.
[38]王立峰, 汪洋, 赵晨, 等. Chebyshev局部配点法在轨迹优化中的应用[J].哈尔滨工业大学学报, 2013, 45(5):95-100.
[39]HUNTINGTON G T, RAO A V. A comparison between global and local orthogonal collocation methods for sol- ving optimal control problems[C]// Proceedings of IEEE 2007 American Control Conference. New York, 2007: 1950-1957.
[40]BEDROSSIAN N, BHATT S. First ever flight demonstration of zero propellant maneuver attitude control concept[C]// AIAA Guidance Navigation and Control Conference and Exhibit. Hitton Head, South Carolina: AIAA, 2007: 123-131.

相似文献/References:

[1]马 杰,梁俊龙.液体冲压发动机技术发展趋势和方向[J].火箭推进,2011,37(04):12.
　MA Jie,LIANG Jun-long.Development trends and directions of liquid ramjet/scramjet technology[J].Journal of Rocket Propulsion,2011,37(05):12.
[2]张敏贵,陈祖奎,靳爱国,等.太阳帆推进[J].火箭推进,2005,31(03):35.
　Zhang Mingui,Chen Zukui,Jin Aiguo.Solar sail[J].Journal of Rocket Propulsion,2005,31(05):35.

备注/Memo

收稿日期：2014-06-30；修回日期：2014-07-23 基金项目：西北工业大学研究生种子基金（Z2014032）和航天支撑基金（NAXA0003） 作者简介：胡松启（1976—），副教授，主要从事固体推进剂及燃烧研究

更新日期/Last Update: 1900-01-01