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

  • Harold L. Stalford
Optimal Control
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3)

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.

Keywords

State Space Optimal Control Problem Function Versus Optimal Control Theory Grad Versus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Leitmann, G., AN INTRODUCTION TO OPTIMAL CONTROL, McGraw Hill, (1966).Google Scholar
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    Pontryagin, L. S., et al., THE MATHEMATICAL THEORY OF OPTIMAL PROCESSING, Interscience Publishers, New York, (1962).Google Scholar
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    Stalford, H., "Sufficiency Conditions in Optimal Control and Differential Games," ORC 70–13, Operations Research Center, University of California, Berkeley, California, 1970.Google Scholar
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    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.Google Scholar
  5. [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.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1973

Authors and Affiliations

  • Harold L. Stalford
    • 1
  1. 1.Naval Research LaboratoryRadar Analysis Staff Radar DivisionWashington

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