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On determining the submanifolds of state space where the optimal value surface has an infinite derivative

  • Optimal Control
  • Conference paper
  • First Online:
5th Conference on Optimization Techniques Part I (Optimization Techniques 1973)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3))

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Abstract

The problem of obtaining the optimal value surface of an optimal control process is investigated. In practice, the optimal cost surface often possesses an infinite derivative at points of certain submanifolds of the state space. A necessary condition is derived with which the equations of such submanifolds can be established without solving first the entire optimal control problem. The necessity of the condition is proved in a theorem, but only for submanifolds having one dimension less than the dimension of the state space. Three examples are provided to illustrate the utility of the condition.

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References

  1. Leitmann, G., AN INTRODUCTION TO OPTIMAL CONTROL, McGraw Hill, (1966).

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  2. Pontryagin, L. S., et al., THE MATHEMATICAL THEORY OF OPTIMAL PROCESSING, Interscience Publishers, New York, (1962).

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  3. Stalford, H., "Sufficiency Conditions in Optimal Control and Differential Games," ORC 70–13, Operations Research Center, University of California, Berkeley, California, 1970.

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  4. Stalford, H., "An Equivalency Optimality Theorem Over a Family of Optimal Control Processes," Proc. of the 1972 Int. Conf. on Cybernetics and Society, IEEE Systems, Man and Cybernetics Society, October 9–12, 1972, Washington, D. C.

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  5. Vincent, T. L., "Pest Management Programs Via Optimal Control Theory," 13th Joint Automatic Control Conference of the American Automatic Control Council, Stanford University, Stanford, California, August 16–18, 1972.

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Authors and Affiliations

  1. Naval Research Laboratory, Radar Analysis Staff Radar Division, 20375, Washington, D. C.

    Harold L. Stalford

Authors
  1. Harold L. Stalford
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R. Conti A. Ruberti

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© 1973 Springer-Verlag Berlin Heidelberg

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Stalford, H.L. (1973). On determining the submanifolds of state space where the optimal value surface has an infinite derivative. In: Conti, R., Ruberti, A. (eds) 5th Conference on Optimization Techniques Part I. Optimization Techniques 1973. Lecture Notes in Computer Science, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-06583-0_27

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  • DOI: https://doi.org/10.1007/3-540-06583-0_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06583-8

  • Online ISBN: 978-3-540-37903-4

  • eBook Packages: Springer Book Archive

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