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Second Variation Conditions for the Optimal Control Problem with Normalized Final Time

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Mechanics and Control

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Abstract

Second variation conditions for the free final time optimal control problem formulated with a normalized final time are derived. This formulation leads to a fixed final time problem with a parameter. The formalism of the neighboring extremal path obtained by the sweep method is used to write the second variation as a perfect square and derive conditions for a minimum. The sufficient conditions are the strengthened Legendre-Clebsch condition, the conjugate point condition, and a condition associated with the parameter.

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References

  1. Bryson, A. E. Jr., and Ho, Y. C., Applied Optimal Control Hemisphere Publishing Corporation, New York, 1975.

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  2. Hull, D. G., “Sufficient Conditions for a Minimum of the Free-Final-Time Optimal Control Problem,” Journal of Optimization Theory and Applications, Vol. 68, No. 2, February, 1991.

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  3. Wood, L. J., “Sufficient Conditions for a Local Minimum of the Bolza Problem with Multiple Terminal Point Constraints,” AAS/AIAA Astrodynamics Specialist Conference, Durango, Colorado, August, 1991.

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  4. Wood, L. J., and Bryson, A. E. Jr., “Second-Order Optimality Conditions for Variable End Time Terminal Control Problems,” AIAA Journal, Vol. 11, No. 9, September, 1973, pp. 1241–1246.

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Author information

Authors and Affiliations

  1. Department of Aerospace Engineering and Engineering Mechanics, The University of Texas Austin, TX, 78712, USA

    David G. Hull

  2. Wright Labs Eglin AFB, FL, 32542, USA

    Christopher N. D’Souza

Authors
  1. David G. Hull
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  2. Christopher N. D’Souza
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Editor information

Editors and Affiliations

  1. University of Southern California, Los Angeles, California, USA

    Ramesh S. Guttalu

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© 1994 Springer Science+Business Media New York

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Hull, D.G., D’Souza, C.N. (1994). Second Variation Conditions for the Optimal Control Problem with Normalized Final Time. In: Guttalu, R.S. (eds) Mechanics and Control. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2425-0_5

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  • DOI: https://doi.org/10.1007/978-1-4615-2425-0_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6029-2

  • Online ISBN: 978-1-4615-2425-0

  • eBook Packages: Springer Book Archive

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