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Legendre pseudospectral method
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Legendre pseudospectral method : ウィキペディア英語版
Legendre pseudospectral method
The Legendre pseudospectral method for optimal control problems is based on Legendre polynomials. It is part of the larger theory of pseudospectral optimal control, a term coined by Ross. The Legendre pseudospectral method was originally proposed by Elnagar and coworkers in 1995.〔G. Elnagar, M. A. Kazemi, and M. Razzaghi, "The Pseudospectral Legendre Method for Discretizing Optimal Control Problems," ''IEEE Transactions on Automatic Control,'' 40:1793–1796, 1995.〕 Since then, Ross, Fahroo and co-workers have analyzed, extended and applied the method for an impressive range of problems.〔Q. Gong, W. Kang, N. Bedrossian, F. Fahroo, P. Sekhavat and K. Bollino, "Pseudospectral Optimal Control for Military and Industrial Applications," ''46th IEEE Conference on Decision and Control,'' New Orleans, LA, pp. 4128–4142, Dec. 2007.〕 An application that has received wide publicity is the use of their method for generating real time trajectories for the International Space Station.
==Software==
The method was first implemented in DIDO in 2001.〔J. R. Rea, ''A Legendre Pseudospectral Method for Rapid Optimization of Launch Vehicle Trajectories,'' S.M. Thesis, Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology, 2001. http://dspace.mit.edu/handle/1721.1/8608〕 Today, it is also available in other software packages such as OTIS and PSOPT.

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