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A note on the use of direct sufficient conditions in optimal control problems

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Abstract

It is always possible to transform a nonautonomous optimal control problem into an autonomous one. However, the direct sufficient conditions may yield no information when applied to this autonomous problem, even though they do allow one to conclude sufficiency when applied to the original nonautonomous problem.

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References

  1. 1.

    Ewing, G. M.,Sufficient Conditions for Global Extrema in the Calculus of Variations, Journal of the Astronautical Sciences, Vol. 12, No. 3, 1965.

  2. 2.

    Mangasarian, O. L.,Sufficient Conditions for the Optimal Control of Nonlinear Systems, SIAM Journal on Control, Vol. 4, No. 1, 1966.

  3. 3.

    Funk, J. E., andGilbert, E. G.,Some Sufficient Conditions for Optimality in Control Problems with State Space Constraints, SIAM Journal on Control, Vol. 8, No. 4, 1970.

  4. 4.

    Leitmann, G., andStalford, H.,A Sufficiency Theorem for Optimal Control, Journal of Optimization Theory and Applications, Vol. 8, No. 3, 1971.

  5. 5.

    Kamien, M. I., andSchwartz, N. L.,Sufficient Conditions in Optimal Control Theory, Journal of Economic Theory, Vol. 3, No. 2, 1971.

  6. 6.

    Peterson, D. W.,A Sufficient Maximum Principle, IEEE Transactions on Automatic Control, Vol. AC-16, No. 1, 1971.

  7. 7.

    Leitmann, G., andSchmitendorf, W. E.,Some Sufficiency Conditions for Pareto-Optimal Control. Journal of Dynamic Systems, Measurement, and Control, Vol. 95, Series G, No. 4, 1973.

  8. 8.

    Schmitendorf, W. E.,A Sufficient Condition for Optimal Control Problems with Time Delays, Automatica, Vol. 9, No. 4, 1973.

  9. 9.

    Stalford, H., andLeitmann, G.,Sufficiency Conditions for Nash Equilibria in N-Person Differential Games, Topics in Differential Games, Edited by A. Blaquiere, North Holland Publishing Company, Amsterdam, Holland, 1973.

  10. 10.

    Mereau, P. M., andPowers, W. F.,A Direct Sufficient Condition for Free-Final-Time Optimal Control Problem, SIAM Journal on Control, Vol. 14, No. 4, 1976.

  11. 11.

    Schmitendorf, W. E.,A Sufficient Condition for Minmax Control of Systems with Uncertainty in the State Equations, IEEE Transactions on Automatic Control, Vol. AC-21, No. 4, 1976.

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Additional information

This research was supported by the Air Force Office of Scientific Research, under Grant No. AFOSR-76-2923.

Communicated by G. Leitmann

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Schmitendorf, W.E. A note on the use of direct sufficient conditions in optimal control problems. J Optim Theory Appl 23, 465–470 (1977). https://doi.org/10.1007/BF00933453

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Key Words

  • Sufficiency theorems
  • optimal control theory
  • control theory
  • optimization theorems