GPOCS

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GPOCS is an implementation of the Gauss pseudospectral method (GPM) for solving multiple-phase optimal control problems. The Gauss pseudospectral method used in GPOCS has been documented extensively in the open literature and has the interesting feature that the adjoints (i.e., costates) of the optimal control problem can be obtained in an algebraically simple way from the KKT multiplers of the GPM nonlinear program. Because of this equivalence, the GPM has been demonstrated to produce highly accurate solutions that can be verified using standard optimal control theory (i.e., optimality conditions from the calculus of variations).

Designed functionally using an approach that is similar to approaches used in other well-known optimal control software programs (e.g., SOCS, GESOP, and DIRCOL) and as described in the work of Betts (see below), the implementation of the GPM in GPOCS enables the user to specify the problem in distinct phases that can be linked in any manner and any order desired. The Gauss pseudospectral method has been tested on many well-known optimal control problems (e.g., supersonic aircraft flight, orbital transfer, and launch vehicle ascent), has been applied to modern formation flying spacecraft trajectory optimization problems, and is continuing to be used in research to solve innovative problems of interest in aerospace engineering.

[edit] References

  • Huntington, Geoffrey T.; Rao, Anil V. (2008). "A Comparison of Local and Global Orthogonal Collocation Methods for Solving Optimal Control Problems". . Journal of Guidance, Control, and Dynamics
  • Benson, David A. (2005-02-01). "A Gauss Pseudospectral Transcription for Optimal Control". . Ph.D. Thesis, Massachusetts Institute of Technology
  • Benson, David A.; Huntington, G. T., Thorvaldsen, T. P., and Rao, A. V. (2006-12-01). "Direct Trajectory Optimization and Costate Estimation via an Orthogonal Collocation Method". . Journal of Guidance, Control, and Dynamics
  • Huntington, Geoffrey T. (2007-05-01). "Advancement and Analysis of a Gauss Pseudospectral Transcription for Optimal Control". . Ph.D. Thesis, Massachusetts Institute of Technology
  • Betts, John T. (2001). Practical Methods for Optimal Control Using Nonlinear Programming. SIAM Press, Philadelphia.