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.[1] The Legendre pseudospectral method was originally proposed by Elnagar and coworkers in 1995.[2] Since then, Ross, Fahroo and co-workers[3][4] have analyzed, extended and applied the method for an impressive range of problems.[5] An application that has received wide publicity[6] 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.[7] Today, it is also available in other software packages such as OTIS and PSOPT.
Flight implementations
The Legendre pseudospectral method has been implemented in flight by NASA several times. The first flight implementation was on November 5, 2006, when NASA used the Legendre pseudospectral method to maneuver the International Space Station to perform the Zero Propellant Maneuver. The Zero Propellant Maneuver was discovered by Nazereth Bedrossian using DIDO. Watch a video of this historic maneuver.
See also
- DIDO
- Chebyshev pseudospectral method
- Ross–Fahroo pseudospectral methods
- Ross–Fahroo lemma
- Covector mapping principle
References
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
- ↑ 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.
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
- ↑ 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.
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
- ↑ 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
