Revisiting Gradient Methods in Function Space - With Application to Rocket Trajectories

Joseph Z. Ben-Asher

2015

Abstract

The gradient method in function space is revisited and applied to the problem of optimizing the trajectories of aerodynamically maneuvering rockets. The optimization objective may be the maximal range or the minimal control effort for a given range. The method is shown to provide an implementable and fast algorithm for a good approximation to the optimal solution. It does not require any non-linear programming solver, and can be straightforwardly programmed in a flight computer. The method can also be used to provide an initial guess for more precise techniques, thus accelerating the computational process.

References

  1. Bryson A. E. and Ho Y-C, Applied Optimal Control, Hemisphere P. C, 1975, pp. 50-120.
  2. Kelley H. J., "Methods of Gradients", Chapter 6 in Optimization Techniques ed. G. Leitman, Academic Press 1962, pp. 218-222.
  3. Stryk O. and Bulirsch R." Direct and Indirect Methods For Trajectory Optimization", Annals of Operations Research 37(1992) 357-373.
  4. Keller H. B., Numerical Methods for Two-Point Boundary Value Problems, Blaisdell, New York, 1968. pp.1-150.
  5. Stryk O., “Numerical Solution of Optimal Control Problems by Direct Collocation, Optimal Control, ed. Bulirsch R, Miele A. and Stoer J., Birkhauser Verlag, Basel, 1993, pp. 129-143..
  6. Benson D. A, Gauss Pseudospectral Transcription for Optimal Control, MIT Ph. D. Thesis, Department of Aeronautics and Astronautics, November 2004.
  7. Elnagar J., Kazemi M. A., and Razzaghi M., “The Pseudospectral Legendre Method for Discretizing Optimal Control Problems,” IEEE Transactions on Automatic Control, Vol. 40, No. 10, October 1995, pp. 1793-1796.
  8. Fahroo F. and Ross I. M., “Costate Estimation by a Legendre Pseudospectral Method,” Journal of Guidance, Control, and Dynamics, Vol. 24, No. 2, 2001, pp. 270-277.
  9. Rao A. V. et.al., “Algorithm 902: GPOPS, A MATLAB Software for Solving Multiple-Phase Optimal Control Problems Using the Gauss Pseudospectral Method”, ACM Transactions on Mathematical Software, Vol. 37, No. 2, Article 22, April 2010.
  10. Bryson A. E. and Denham W. F. “A Steepest-Ascent Method for Solving Optimum Programming Problems,” J. Appl. Mech. 29(2), 247-257, 2011.
  11. Kelley H. J., Cliff E. M. and Lutze, F. H, “Boost-glide Range-Optimal Guidance,” Optimal Control Applications and Methods, Volume 3, Issue 3, pages 293-298, July-September 1982.
  12. Courant R. and Hilbert D., Methods of Mathematical Physics vol.X , Interscience Publishers Inc. 1953, pp. 222-224.
  13. Bryson A. E., Dynamic Optimization, Addison Wesley Longman, 1999.
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Paper Citation


in Harvard Style

Ben-Asher J. (2015). Revisiting Gradient Methods in Function Space - With Application to Rocket Trajectories . In Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-758-122-9, pages 270-274. DOI: 10.5220/0005562702700274


in Bibtex Style

@conference{icinco15,
author={Joseph Z. Ben-Asher},
title={Revisiting Gradient Methods in Function Space - With Application to Rocket Trajectories},
booktitle={Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2015},
pages={270-274},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005562702700274},
isbn={978-989-758-122-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - Revisiting Gradient Methods in Function Space - With Application to Rocket Trajectories
SN - 978-989-758-122-9
AU - Ben-Asher J.
PY - 2015
SP - 270
EP - 274
DO - 10.5220/0005562702700274