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An elementary derivation of Pontrayagin's maximum principle of optimal control theory

Published online by Cambridge University Press:  17 February 2009

J. M. Blatt  and
J. D. Gray
J. M. Blatt
Affiliation:
School of Mathematics, University of New South Wales, Kensington, N.S.W. 2033, Australia
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Abstract

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Pontryagin's maximum principle is derived by elementary mathematical techniques. The conditions on the functions which enter are generally somewhat more stringent than in Pontryagin's derivation, but one (practically very awkward) condition of Pontryagin can be relaxed: continuity in the time variable can be replaced by a much weaker condition.

Type
Research Article
Information
The ANZIAM Journal , Volume 20 , Issue 2 , December 1977 , pp. 142 - 156
Copyright
Copyright © Australian Mathematical Society 1977

References

REFERENCES

[1]Agnew, R. P., Differential equations (McGraw-Hill, New York and London, 1942). (See in particular Chapter 15.)Google Scholar
[2]Blatt, J. M., “Heating your house with control theory” (unpublished).Google Scholar
[3]Bryant, G. F. and Mayne, D. O., “The maximum principle”, Int. J. Control, 20 (1974), 1021–1054.CrossRefGoogle Scholar
]Gamkrelidze, R. V., “Extremal problems in finite dimensional spaces”, J. Optimization Th. Appl. 1 (1967), 173–193;CrossRefGoogle Scholar
and Berkovitz, L. D., “Variational methods in problems of control and programming”, J. Math. Anal. Applic. 3 (1961), 145–169;CrossRefGoogle Scholar
and Lawden, D. F., Optimal trajectories for space navigation (Butterworths, London, 1963), Section 1.9.Google Scholar
[5]Hadley, G. and Kemp, M. C., Variational methods in economics (American Elsevier Publishing Co., Inc., New York; North-Holland Publishing Co., Amsterdam-London, 1971).Google Scholar
[6]Halkin, H. in Leitmann, C. (ed.), Topics in optimization (Academic Press, New York and London, 1967), pp. 197–262.CrossRefGoogle Scholar
[7]Halkin, H. and Neustadt, L. W., “General necessary conditions for optimization problems”, Proc. Nat. Acad. Sci. U.S.A. 56 (1966), 1066–1071.CrossRefGoogle ScholarPubMed
[8]Pontryagin, L. S., Boltyanskii, V. G., Gramkrelidze, R. V. and Mischenko, E. F., The mathematical theory of optimal processes (Interscience Publishers, Inc., New York, 1962).Google Scholar