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解一类最优控制问题的一种自适应拟谱方法 被引量：1

An Adaptive Pseudospectral Method for Solving a Class of Optimal Control Problems
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摘要 提出一种解常微分方程最优控制问题的自适应拟谱方法.对状态函数和控制函数使用不同次数的多项式逼近.设计了一个自适应算法决定不同的次数,并给出了理论分析.数值算例比较了本文方法与一种常用的拟谱方法. An adaptive pseudospectral method is proposed to solve optimal control problems governed by ordinary differential equations.The polynomials approximating the state and control functions can have the different degrees.An adaptive algorithm is designed in order to determine the different degrees,and theoretical analysis is given.The proposed method is compared with a widely applied pseudo spectral method by numerical examples.
作者 秦廷华 马和平
机构地区 上海大学理学院数学系
出处 《信息与控制》 CSCD 北大核心 2012年第5期583-589,共7页 Information and Control
基金 国家自然科学基金资助项目(11171209)
关键词 拟谱方法 最优控制 非线性规划 自适应 pseudospectral method optimal control nonlinear programming adaptive
分类号 TP273.1 [自动化与计算机技术—检测技术与自动化装置]
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参考文献20

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同被引文献19

  • 1Hunington G T. Advancement and analysis of a guass pseuospectral transcription for optimal control[D]. Cambridge: Massachusetts Institute of Technology, 2007.
  • 2Benson D A. A Gauss pseudospectral transcription for optimal control[D]. Cambridge: Massachusetts institute Technoligy, 2004.
  • 3Sun Y, Zhang M R, Li H. Now costato estimation of Gauss pseudospectral method for nonlinear optimal control problem[C]//Proceeding of the 2011 International Workshop on Engineering Application Research. Hangzhou, China: IEIT, 2011: 31-36.
  • 4Gong Q, Fahroo F, Ross I M. Spectral algorithm for pseudospectral methods in optimal control[J]. Journal of Guidance, Control, and Dynamics, 2008, 31(3): 460-471.
  • 5Darby G L, Hager W W, Rao A V. Direct trajectory optimization using a variable low-order adaptive pseudospectral method[J]. Journal of Spacecraft and Rockets, 2011, 48(3): 433-445.
  • 6Qi G, Ross I M. Autonomous pseudospectral knotting methods for space mission optimizaition[C]//Proceeding of the AAS/AIAA Space Flight Mechanics Meeting. Reston: AIAA, 2006: 779-794.
  • 7Jain S, Tsiotras P. Trajectory optimization using multiresolution techniques[J]. Journal of Guidance, Control, and Dynamics, 2008, 31(5): 1424-1436.
  • 8Darby G L, Hager W W, Rao A V. An hp-adaptive pseudospectral method for solving optimal problems[J]. Optimal Control Applications and Methods, 2011, 32(4): 476-502.
  • 9Ross I M, Fahroo F. A perspective on methods for trajectory optimization[C]//Proceedings of AIAA/AAS Astrodynamics Specialist Conference and Exhibit. Reston: AIAA, 2007: 831-839.
  • 10Lu P, Pan B F. Highly constrained optimal launch ascent guidance[J]. Journal of Guidance, Control, and Dynamics, 2010, 33(2): 404-414.

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信息与控制
2012年 第5期

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