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An exact penalty function algorithm for optimal control problems with control and terminal equality constraints, part 2

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Abstract

In Part 1 of this paper, implementable and conceptual versions of an algorithm for optimal control problems with control constraints and terminal equality constraints were presented. It was shown that anyL ∞ accumulation points of control sequences generated by the algorithms satisfy necessary conditions of optimality. Since such accumulation points need not exist, it is shown in this paper that control sequences generated by the algorithms always have accumulation points in the sense of control measure, and these accumulation points satisfy optimality conditions for the corresponding relaxed control problem.

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References

  1. Williamson, L. J., andPolak, E.,Relaxed Controls and the Convergence of Optimal Control Algorithms, SIAM Journal on Control and Optimization, Vol. 14, No. 4, 1976.

  2. Warga, J.,Optimal Control of Differential and Functional Equations, Academic Press, New York, New York, 1973.

    Google Scholar 

  3. Young, L. C.,Lectures on the Calculations of Variations and Optimal Control Theory, W. B. Saunders Company, New York, New York, 1969.

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  4. Canon, M. D., Cullum, C. D., andPolak, E.,Theory of Optimal Control and Mathematical Programming, McGraw-Hill Book Company, New York, New York, 1970.

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  5. Demyanov, V. F., andMalzemov, V. N.,Introduction to Minimax, John Wiley and Sons, New York, New York, 1974.

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  6. Polak, E.,Computational Methods in Optimization, Academic Press, New York, New York, 1971.

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Author information

Authors and Affiliations

  1. Department of Computing and Control, Imperial College of Science and Technology, London, England

    D. Q. Mayne (Professor)

  2. Department of Electrical Engineering and Computer Science and Electronics Research Laboratory, University of California, Berkeley, California

    E. Polak (Professor)

Authors
  1. D. Q. Mayne
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  2. E. Polak
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Additional information

Communicated by P. Varaiya

This work was supported by the United Kingdom Science Research Council, by the US Army Research Office, Contract No. DAA-29-73-C-0025, and by the National Science Foundation, Grant No. ENG-73-08214-A01.

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Mayne, D.Q., Polak, E. An exact penalty function algorithm for optimal control problems with control and terminal equality constraints, part 2. J Optim Theory Appl 32, 345–364 (1980). https://doi.org/10.1007/BF00934557

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