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Additional necessary conditions for optimal control with state-variable inequality constraints

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Abstract

It is shown that, when the set of necessary conditions for an optimal control problem with state-variable inequality constraints given by Bryson, Denham, and Dreyfus is appropriately augmented, it is equivalent to the (different) set of conditions given by Jacobson, Lele, and Speyer. Relationships among the various multipliers are given.

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References

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    Jacobson, D. H., Lele, M. M., andSpeyer, J. L.,New Necessary Conditions of Optimality for Control Problems with State-Variable Inequality Constraints, Journal of Mathematical Analysis and Applications, Vol. 34, pp. 255–284, 1971.

  2. 2.

    Bryson, A. E., Jr., Denham, W. F., andDreyfus, S. E.,Optimal Programming Problems with Inequality Constraints, I: Necessary Conditions for Extremal Solutions, AIAA Journal, Vol. 1, pp. 2544–2550, 1963.

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    Bryson, A. E., Jr., andHo, Y. C.,Applied Optimal Control (Revised Printing), John Wiley and Sons, New York, New York, 1975.

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    Norris, D. O.,Nonlinear Programming Applied to State-Constrained Optimization Problems, Journal of Mathematical Analysis and Applications, Vol. 43, pp. 261–272, 1973.

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    Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., andMishchenko, E. F.,The Mathematical Theory of Optimal Processes, John Wiley and Sons, New York, New York, 1962.

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    McIntyre, J., andPaiewonsky, B.,On Optimal Control with Bounded State Variables, Advances in Control Systems, Vol. 5, Edited by C. T. Leondes, Academic Press, New York, New York, 1967.

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    Taylor, J. G.,Comments on a Multiplier Condition for Problems with State Inequality Constraints, IEEE Transactions on Automatic Control, Vol. AC-17, pp. 743–744, 1972.

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Additional information

This work was done at NASA Ames Research Center, Moffett Field, California, under a National Research Council Associateship.

Communicated by J. V. Breakwell

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Kreindler, E. Additional necessary conditions for optimal control with state-variable inequality constraints. J Optim Theory Appl 38, 241–250 (1982). https://doi.org/10.1007/BF00934086

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Key Words

  • Optimal control
  • state constraints
  • necessary conditions for optimality