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On the order of singular optimal control problems

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Abstract

In singular optimal control problems, the functional form of the optimal control function is usually determined by solving the algebraic equation which results by successively differentiating the switching function until the control appears explicitly. This process defines the order of the singular problem. Order-related results are developed for singular linear-quadratic problems and for a bilinear example which gives new insights into the relationship between singular problem order and singular are order.

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References

  1. Kelley, H. J.,A Second Variation Test for Singular Extremals, AIAA Journal Vol. 2, No. 8, 1964.

  2. Kopp, R. E., andMoyer, H. G.,Necessary Conditions for Singular Extremals, AIAA Journal, Vol. 3, No. 8, 1965.

  3. Kelley, H. J., Kopp, R. E., andMoyer, H. G.,Singular Extremals, Topics In Optimization, Edited by G. Leitmann, Academic Press, New York, New York, 1967.

    Google Scholar 

  4. Robbins, H. M.,A Generalized Legendre-Clebsch Condition for the Singular Cases of Optimal Control, IBM Journal, Vol. 11, pp. 361–372, 1967.

    Google Scholar 

  5. McDanell, J. P., andPowers, W. F.,Necessary Conditions for Joining Optimal Singular and Nonsingular Subarcs, SIAM Journal on Control, Vol. 9, No. 2, 1971.

  6. Krener, A. J.,The High-Order Maximum Principle and Its Application to Singular Extremals, SIAM Journal on Control, Vol. 15, pp. 256–293, 1977.

    Google Scholar 

  7. Rebhuhn, D.,On the Stability of the Existence of Singular Controls under Perturbation of the Control System, SIAM Journal on Control, Vol. 16, pp. 463–472, 1978.

    Google Scholar 

  8. Lewis, R. M.,Definitions of Order and Junction Conditions in Singular Optimal Control Problems, SIAM Journal on Control, Vol. 18, No. 1, 1979.

  9. Bell, D. J., andJacobson, D. H.,Singular Optimal Control Problems, Academic Press, New York, New York, 1975.

    Google Scholar 

  10. Bortins, R., Boustany, N. M., andPowers, W. F.,The Infinite-Order Singular Problem, University of Michigan, CICE Report No. 80-1, 1980.

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Authors and Affiliations

  1. Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan

    W. F. Powers (Professor)

  2. Control Systems Department, Research, Ford Motor Company, Dearborn, Michigan

    W. F. Powers (Professor)

Authors
  1. W. F. Powers
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Dedicated to R. Bellman

This work was supported by the National Science Foundation under Grant No. ENG-77-16660.

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Powers, W.F. On the order of singular optimal control problems. J Optim Theory Appl 32, 479–489 (1980). https://doi.org/10.1007/BF00934035

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  • DOI: https://doi.org/10.1007/BF00934035

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