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Legendre pseudospectral method

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The Legendre pseudospectral method for optimal control problems is based on Legendre polynomials. It is part of the larger pseudospectral optimal control theory, that was originally proposed by Elnagar and coworkers in 1995.[1] Since then, Ross, Fahroo and co-workers[2][3] have analysed, extended and applied the method for an impressive range of problems. An application that has received wide publicity is the use of their method for generating real time trajectories for the International Space Station.[4]

Software

The method was first implemented in DIDO in 2001. Today, it is also available in other software packages such as OTIS and PSOPT.


References

  1. ^ 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.
  2. ^ W. Kang, Q. Gong, I. M. Ross, and F. Fahroo. On the Convergence of Nonlinear Optimal Control Using Pseudospectral Methods for Feedback Linearizable Systems. International Journal of Robust and Nonlinear Control, 17:1251–1277, 2007.
  3. ^ I. M. Ross and F. Fahroo. Pseudospectral Knotting Methods for Solving Nonsmooth Optimal Control Problems. Journal of Guidance Control and Dynamics, 27:397–405, 2004.
  4. ^ W. Kang and N. Bedrossian. Pseudospectral Optimal Control Theory Makes Debut Flight, Saves nasa $1m in Under Three Hours. SIAM News, 40, 2007.
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