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On general problems with bounded state variables

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Abstract

This paper serves as the sequel to a recent article by the author concerned with a certain canonical control problem. The present paper extends the first-order necessary conditions obtained there to a general form of the control problem of Bolza with inequality state constraints of the type ψα(t, x)≤0, α=1,...,m.

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References

  1. 1.

    Russak, I. B.,On Problems with Bounded State Variables, Journal of Optimization Theory and Applications, Vol. 5, No. 2, 1970.

  2. 2.

    Russak, I. B.,On Problems with Bounded State Variables, University of California at Los Angeles, Ph.D. Thesis, 1967.

  3. 3.

    Hestenes, M. R.,Calculus of Variations and Optimal Control Theory, John Wiley and Sons, New York, 1966.

Additional Bibliography

  1. 4.

    Hestenes, M. R.,On Variational Theory and Optimal Control Theory, SIAM Journal on Control, Vol. 3, No. 1, 1965.

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Additional information

The preparation of this paper was sponsored in part by the U.S. Army Research Office under Grant No. DA-31-124-ARO(D)-355.

Communicated by M. R. Hestenes

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Russak, I.B. On general problems with bounded state variables. J Optim Theory Appl 6, 424–452 (1970). https://doi.org/10.1007/BF00932720

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Keywords

  • Bounded State
  • Control Problem
  • General Problem
  • Recent Article
  • State Constraint